<Text-field style="Heading 1" layout="Heading 1">Problem 5-8</Text-field>

<Text-field style="Heading 1" layout="Heading 1">Solution</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Cross-Section of the Cylinder</Text-field>

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Enter LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKCZtaW51cztGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkctSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiRGK0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Yv.

Context Menu: Plots\342\211\273Plot Builder Adjust the plot window appropriately.

Control-drag LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= onto the graph.

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plot(, x = 0 .. 2);

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<Text-field style="Heading 2" layout="Heading 2">Data Entry</Text-field>

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Control-drag the equation 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 Context Menu: Assign Name

Control-drag the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlgtRkQ2LVEpJmhlbGxpcDtGJ0Y+RkdGSkZMRk5GUEZSRlQvRldRLDAuMTY2NjY2N2VtRicvRlpGaW5GPg== Context Menu: Assign Name

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plots[display](plot3d(7-x^2-y^2, x = 0 .. 1, y = x .. 2-x^2, filled = true), plot3d(x+y-3, x = 0 .. 1, y = x .. 2-x^2, filled = true), axes = boxed);

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<Text-field style="Heading 2" layout="Heading 2">Iterated Double Integral - Visualization</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Multivariate\342\211\273Integration\342\211\273Visualizing Regions of Integration\342\211\273Cartesian 2-D

Evaluate 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 and Graph LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=

Area Element LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEjZEFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn

Select dA,dy dx,dx dyuse DocumentTools in IntOrder := module() local Y,q1,g,G,a,b,x,y,Psi,q2; export X; q1 := Int(Psi,[y=g(x)..G(x), x=a..b]); q2 := Int(Psi,[x=g(y)..G(y), y=a..b]); Y := GetProperty(ComboBox1,value); if Y = "dy dx" then X:=1; Do(%MathContainer9 = q1); elif Y = "dx dy" then X:=2; Do(%MathContainer9 = q2); elif Y = "Select dA" then X:=3; Do(%MathContainer9 = NULL); end if; end module; end use;

, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5MzY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSUYy

use DocumentTools in Do(%MathContainer10 = NULL); end use;

Value of Integral

use DocumentTools in module() local f,F,g,G,a,b,q, P, s1; if GetProperty(ComboBox1,value) = "Select dA" then Do(%MathContainer9 = MathML[Export]("Select an area element"));return;end if; try exports(IntOrder); catch : SetProperty(ComboBox1, value, "Select dA"); Do(%MathContainer9 = MathML[Export]("Initialize by re-selecting area element")); Do(%MathContainer11 = NULL); return; end try; Do(G = %MathContainer12); Do(g = %MathContainer14); Do(b = %MathContainer13); Do(a = %MathContainer15); Do(P = %MathContainer10); if nops([P])=0 then Do(%MathContainer11 = MathML[Export]("Please provide an integrand")); return; end if; if nops([G])=0 then Do(%MathContainer11 = MathML[Export]("Please provide G")); return; end if; if nops([g])=0 then Do(%MathContainer11 = MathML[Export]("Please provide g")); return; end if; if nops([b])=0 then Do(%MathContainer11 = MathML[Export]("Please provide b")); return; end if; if nops([a])=0 then Do(%MathContainer11 = MathML[Export]("Please provide a")); return; end if; if IntOrder:-X = 1 then s1 := {x}; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer11 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer11 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer11 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer11 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[y=g..G, x=a..b]); elif IntOrder:-X = 2 then s1 := {y}; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer11 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer11 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer11 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer11 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[x=g..G, y=a..b]); else return; end if; Do(%MathContainer11 = value(q)); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer12 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer13 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer14 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer15 = NULL); end use;

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use DocumentTools, plots, VectorCalculus in module() local F,g,G,a,b, FF, gg, GG, P, bot, top, lft, rgt, fnt, bck, s2, s1, p1,p3,p4,p5,p6, m, gm, Gm, q1,q2,q3,q4,q5,q6; if GetProperty(ComboBox1,value) = "Select dA" then Do(%Plot2 = display(textplot([0,0,"Please select an area element"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; try exports(IntOrder); catch : SetProperty(ComboBox1,value,"Select dA"); Do(%MathContainer9 = NULL); Do(%Plot2 = display(textplot([0,0,"Initialize by re-selecting an area element"],font=[TIMES,ROMAN,14]),axes=none));return; end try; Do(FF = %MathContainer10); Do(GG = %MathContainer12); Do(gg = %MathContainer14); Do(b = %MathContainer13); Do(a = %MathContainer15); if nops([FF])=0 then Do(%Plot2 = display(textplot([0,0,"Please provide an integrand"],font=[TIMES,ROMAN,14]),axes=none));return;end if; if nops([GG])=0 then Do(%Plot2 = display(textplot([0,0,"Please provide G"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([gg])=0 then Do(%Plot2 = display(textplot([0,0,"Please provide g"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([b])= 0 then Do(%Plot2 = display(textplot([0,0,"Please provide b"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([a])= 0 then Do(%Plot2 = display(textplot([0,0,"Please provide a"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; p1 := display(textplot([0,0," "]),axes=none); p3 := display(textplot([0,0,"Check variables in g"],font=[TIMES,ROMAN,14]),axes=none); p4 := display(textplot([0,0,"Check variables in G"],font=[TIMES,ROMAN,14]),axes=none); p5 := display(textplot([0,0,"Lower limit 'a' must be numeric"],font=[TIMES,ROMAN,14]),axes=none); p6 := display(textplot([0,0,"Upper limit 'b' must be numeric"],font=[TIMES,ROMAN,14]),axes=none); F := unapply(FF,(x,y)); if IntOrder:-X = 1 then s1 := {x}; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%Plot2 = p3);Do(%Plot1 = p1);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%Plot2 = p4);Do(%Plot1 = p1);return;end if; if not type(evalf(a),numeric) then Do(%Plot2 = p5);Do(%Plot1 = p1);return;end if; if not type(evalf(b),numeric) then Do(%Plot2 = p6);Do(%Plot1 = p1);return;end if; g := unapply(gg,x); G := unapply(GG,x); bot := plot3d([x,y,0],x=a..b,y=g(x)..G(x),color=blue): top := plot3d([x,y,F(x,y)],x=a..b,y=g(x)..G(x),color=red): lft := plot3d([x,g(x),z],x=a..b,z=0..F(x,g(x)),color=green): rgt := plot3d([x,G(x),z],x=a..b,z=0..F(x,G(x)),color=gold): fnt := plot3d([b,y,z],y=g(b)..G(b),z=0..F(b,y),color=gray): bck := plot3d([a,y,z],y=g(a)..G(a),z=0..F(a,y),color=yellow): elif IntOrder:-X = 2 then s1 := {y}; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%Plot2 = p3);Do(%Plot1 = p1);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%Plot2 = p4);Do(%Plot1 = p1);return;end if; if not type(evalf(a),numeric) then Do(%Plot2 = p5);Do(%Plot1 = p1);return;end if; if not type(evalf(b),numeric) then Do(%Plot2 = p6);Do(%Plot1 = p1);return;end if; g := unapply(gg,y); G := unapply(GG,y); bot := plot3d([x,y,0],y=a..b,x=g(y)..G(y),color=blue): top := plot3d([x,y,F(x,y)],y=a..b,x=g(y)..G(y),color=red): lft := plot3d([x,a,z],x=g(a)..G(a),z=0..F(x,a),color=yellow): rgt := plot3d([x,b,z],x=g(b)..G(b),z=0..F(x,b),color=gray): bck := plot3d([g(y),y,z],y=a..b,z=0..F(g(y),y),color=green): fnt := plot3d([G(y),y,z],y=a..b,z=0..F(G(y),y),color=gold): else return; end if; P := display([bot,top,lft,rgt,fnt,bck],axes=box,labels=[x,y,z],orientation=[-115,80],style=surface); Do(%Plot2 = P); m := (a+b)/2; gm := g(m); Gm := G(m); if IntOrder:-X = 1 then q1 := plot(g(x),x=a..b,color=red,legend=typeset(Typesetting:-mi("g"))): q2 := plot(G(x),x=a..b,color=black,legend=typeset(Typesetting:-mi("G"))): q3 := PlotVector(RootedVector(root=[m,gm],[0,Gm-gm]),color="Orange",width=[.05,relative=false]): q4 := plot([[a,g(a)],[a,G(a)]],style=line, color=cyan): q5 := plot([[b,g(b)],[b,G(b)]],style=line, color=cyan): q6 := display([q1,q2,q3,q4,q5],labels=[x,y]); else q1 := plot([g(y),y,y=a..b], color=red,legend=typeset(Typesetting:-mi("g"))): q2 := plot([G(y),y,y=a..b], color=black, legend=typeset(Typesetting:-mi("G"))): q3 := PlotVector(RootedVector(root=[gm,m],[Gm-gm,0]),color="Orange",width=[.05,relative=false]): q4 := plot([[g(a),a],[G(a),a]],style=line, color=cyan): q5 := plot([[g(b),b],[G(b),b]],style=line, color=cyan): q6 := display([q1,q2,q3,q4,q5],labels=[x,y]); end if; Do(%Plot1 = q6); end module; end use;

use DocumentTools, plots in module() local p; p := display(textplot([0,0," "]),axes=none); Do(%Plot1 = p); Do(%Plot2 = p); end module; end use;

use DocumentTools, plots in module() local p; p := display(textplot([0,0," "]),axes=none); Do(%Plot1 = p); Do(%Plot2 = p); SetProperty(ComboBox1, value, "Select dA"); Do(%MathContainer9 = NULL); Do(%MathContainer10 = NULL); Do(%MathContainer12 = NULL); Do(%MathContainer14 = NULL); Do(%MathContainer13 = NULL); Do(%MathContainer15 = NULL); Do(%MathContainer11 = NULL); end module; end use;

Bounding Curves

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"Volume"

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 2" layout="Heading 2">Iterated Double Integral - Integration Details</Text-field>

JSFH

Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Multivariate\342\211\273Integration\342\211\273Multiple Integration\342\211\273Cartesian 2-D

Iterated Double Integral in Cartesian Coordinates

Integrand:

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Region: 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Inert integral: LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYlUSFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSVtcm93R0YkNiYtRiw2JVEjZHlGJ0YvRjItSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZDLyUpc3RyZXRjaHlHRkMvJSpzeW1tZXRyaWNHRkMvJShsYXJnZW9wR0ZDLyUubW92YWJsZWxpbWl0c0dGQy8lJ2FjY2VudEdGQy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlItRiw2JVEjZHhGJ0YvRjJGP0YrRj8=

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Value:

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

Stepwise Evaluation:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 2" layout="Heading 2">Iterated Triple Integral - Visualization</Text-field>

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Tools\342\211\273Tasks\342\211\273Browse:

Calculus - Multivariate\342\211\273Integration\342\211\273Visualizing Regions of Integration\342\211\273Cartesian 3-D

Evaluate 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 and Graph LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=

Volume Element LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn

Select dv,dz dy dx,dz dx dy,dx dy dz,dx dz dy,dy dx dz,dy dz dxuse DocumentTools in IntOrder := module() local Y,q1,f,F,g,G,x,y,z,a,b,Psi,q2,q3,q4,q5,q6; export X; q1 := Int(Psi,[z=f(x,y)..F(x,y), y=g(x)..G(x), x=a..b]); q2 := Int(Psi,[z=f(x,y)..F(x,y), x=g(y)..G(y), y=a..b]); q3 := Int(Psi,[x=f(y,z)..F(y,z), y=g(z)..G(z), z=a..b]); q4 := Int(Psi,[x=f(y,z)..F(y,z), z=g(y)..G(y), y=a..b]); q5 := Int(Psi,[y=f(x,z)..F(x,z), x=g(z)..G(z), z=a..b]); q6 := Int(Psi,[y=f(x,z)..F(x,z), z=g(x)..G(x), x=a..b]); Y := GetProperty(ComboBox0,value); if Y = "dz dy dx" then X:=1; Do(%MathContainer0 = q1); elif Y = "dz dx dy" then X:=2; Do(%MathContainer0 = q2); elif Y = "dx dy dz" then X:=3; Do(%MathContainer0 = q3); elif Y = "dx dz dy" then X:=4; Do(%MathContainer0 = q4); elif Y = "dy dx dz" then X:=5; Do(%MathContainer0 = q5); elif Y = "dy dz dx" then X:=6; Do(%MathContainer0 = q6); elif Y = "Select dv" then X:=7; Do(%MathContainer0 = NULL); end if; end module; end use;

, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5MzY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSUYy

use DocumentTools in Do(%MathContainer1 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer2 = NULL); end use;

use DocumentTools in Do(%MathContainer3 = NULL); end use;

use DocumentTools in Do(%MathContainer4 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5

use DocumentTools in Do(%MathContainer5 = NULL); end use;

use DocumentTools in Do(%MathContainer6 = NULL); end use;

use DocumentTools in Do(%MathContainer7 = NULL); end use;

use DocumentTools in module() local f,F,g,G,a,b,q, P, s1,s2; if GetProperty(ComboBox0,value) = "Select dv" then Do(%MathContainer0 = MathML[Export]("Select a volume element"));return;end if; try exports(IntOrder); catch : SetProperty(ComboBox0, value, "Select dv"); Do(%MathContainer0 = MathML[Export]("Initialize by re-selecting volume element")); Do(%MathContainer8 = NULL); return; end try; Do(F = %MathContainer2); Do(f = %MathContainer5); Do(G = %MathContainer3); Do(g = %MathContainer6); Do(b = %MathContainer4); Do(a = %MathContainer7); Do(P = %MathContainer1); if nops([P])=0 then Do(%MathContainer8 = MathML[Export]("Please provide an integrand")); return; end if; if nops([F])=0 then Do(%MathContainer8 = MathML[Export]("Please provide F")); return; end if; if nops([f])=0 then Do(%MathContainer8 = MathML[Export]("Please provide f")); return; end if; if nops([G])=0 then Do(%MathContainer8 = MathML[Export]("Please provide G")); return; end if; if nops([g])=0 then Do(%MathContainer8 = MathML[Export]("Please provide g")); return; end if; if nops([b])=0 then Do(%MathContainer8 = MathML[Export]("Please provide b")); return; end if; if nops([a])=0 then Do(%MathContainer8 = MathML[Export]("Please provide a")); return; end if; if IntOrder:-X = 1 then s2 := {x,y}; s1 := {x}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[z=f..F, y=g..G, x=a..b]); elif IntOrder:-X = 2 then s2 := {x,y}; s1 := {y}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[z=f..F, x=g..G, y=a..b]); elif IntOrder:-X = 3 then s2 := {y,z}; s1 := {z}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[x=f..F, y=g..G, z=a..b]); elif IntOrder:-X = 4 then s2 := {y,z}; s1 := {y}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[x=f..F, z=g..G, y=a..b]); elif IntOrder:-X = 5 then s2 := {x,z}; s1 := {z}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[y=f..F, x=g..G, z=a..b]); elif IntOrder:-X = 6 then s2 := {x,z}; s1 := {x}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[y=f..F, z=g..G, x=a..b]); else return; end if; Do(%MathContainer8 = value(q)); end module; end use;

use DocumentTools in module() local f,F,g,G,a,b,q, P; if GetProperty(ComboBox0,value) = "Select dv" then Do(%MathContainer0 = MathML[Export]("Select a volume element"));return;end if; try exports(IntOrder); catch : SetProperty(ComboBox0, value, "Select dv"); Do(%MathContainer0 = MathML[Export]("Initialize by re-selecting volume element")); Do(%MathContainer8 = NULL); return; end try; Do(F = %MathContainer2); Do(f = %MathContainer5); Do(G = %MathContainer3); Do(g = %MathContainer6); Do(b = %MathContainer4); Do(a = %MathContainer7); Do(P = %MathContainer1); if nops([F])=0 then Do(%MathContainer8 = MathML[Export]("Please provide F")); return; end if; if nops([f])=0 then Do(%MathContainer8 = MathML[Export]("Please provide f")); return; end if; if nops([G])=0 then Do(%MathContainer8 = MathML[Export]("Please provide G")); return; end if; if nops([g])=0 then Do(%MathContainer8 = MathML[Export]("Please provide g")); return; end if; if nops([b])=0 then Do(%MathContainer8 = MathML[Export]("Please provide b")); return; end if; if nops([a])=0 then Do(%MathContainer8 = MathML[Export]("Please provide a")); return; end if; if nops([P])=0 then Do(%MathContainer8 = MathML[Export]("Please provide an integrand")); return; end if; if IntOrder:-X = 1 then s2 := {x,y}; s1 := {x}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[z=f..F, y=g..G, x=a..b]); elif IntOrder:-X = 2 then s2 := {x,y}; s1 := {y}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[z=f..F, x=g..G, y=a..b]); elif IntOrder:-X = 3 then s2 := {y,z}; s1 := {z}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[x=f..F, y=g..G, z=a..b]); elif IntOrder:-X = 4 then s2 := {y,z}; s1 := {y}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[x=f..F, z=g..G, y=a..b]); elif IntOrder:-X = 5 then s2 := {x,z}; s1 := {z}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[y=f..F, x=g..G, z=a..b]); elif IntOrder:-X = 6 then s2 := {x,z}; s1 := {x}; if nops(select(type,indets(f),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in f"));return;end if; if nops(select(type,indets(F),name) minus s2)>0 then Do(%MathContainer8 = MathML[Export]("Check variables in F"));return;end if; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer8 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P,[y=f..F, z=g..G, x=a..b]); else return; end if; Do(%MathContainer8 = evalf(q)); end module; end use;

use DocumentTools, plots in module() local f,F,g,G,a,b, ff, FF, gg, GG, P, bot, top, lft, rgt, fnt, bck, s2, s1, p1,p2,p3,p4,p5,p6; if GetProperty(ComboBox0,value) = "Select dv" then Do(%Plot0 = display(textplot([0,0,"Please select a volume element"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; try exports(IntOrder); catch : SetProperty(ComboBox0,value,"Select dv"); Do(%MathContainer0 = NULL); Do(%Plot0 = display(textplot([0,0,"Initialize by re-selecting a volume element"],font=[TIMES,ROMAN,14]),axes=none));return; end try; Do(FF = %MathContainer2); Do(ff = %MathContainer5); Do(GG = %MathContainer3); Do(gg = %MathContainer6); Do(b = %MathContainer4); Do(a = %MathContainer7); if nops([FF])=0 then Do(%Plot0 = display(textplot([0,0,"Please provide F"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([ff])=0 then Do(%Plot0 = display(textplot([0,0,"Please provide f"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([GG])=0 then Do(%Plot0 = display(textplot([0,0,"Please provide G"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([gg])=0 then Do(%Plot0 = display(textplot([0,0,"Please provide g"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([b])= 0 then Do(%Plot0 = display(textplot([0,0,"Please provide b"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([a])= 0 then Do(%Plot0 = display(textplot([0,0,"Please provide a"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; p1 := display(textplot([0,0,"Check variables in f"],font=[TIMES,ROMAN,14]),axes=none); p2 := display(textplot([0,0,"Check variables in F"],font=[TIMES,ROMAN,14]),axes=none); p3 := display(textplot([0,0,"Check variables in g"],font=[TIMES,ROMAN,14]),axes=none); p4 := display(textplot([0,0,"Check variables in G"],font=[TIMES,ROMAN,14]),axes=none); p5 := display(textplot([0,0,"Lower limit 'a' must be numeric"],font=[TIMES,ROMAN,14]),axes=none); p6 := display(textplot([0,0,"Upper limit 'b' must be numeric"],font=[TIMES,ROMAN,14]),axes=none); if IntOrder:-X = 1 then s2 := {x,y}; s1 := {x}; if nops(select(type,indets(ff),name) minus s2)>0 then Do(%MathContainer8 = p1);return;end if; if nops(select(type,indets(FF),name) minus s2)>0 then Do(%MathContainer8 = p2);return;end if; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%MathContainer8 = p3);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%MathContainer8 = p4);return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = p5);return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = p6);return;end if; f := unapply(ff,(x,y)); F := unapply(FF,(x,y)); g := unapply(gg,x); G := unapply(GG,x); bot := plot3d([x,y,f(x,y)],x=a..b,y=g(x)..G(x),color=blue): top := plot3d([x,y,F(x,y)],x=a..b,y=g(x)..G(x),color=red): lft := plot3d([x,g(x),z],x=a..b,z=f(x,g(x))..F(x,g(x)),color=green): rgt := plot3d([x,G(x),z],x=a..b,z=f(x,G(x))..F(x,G(x)),color=gold): fnt := plot3d([b,y,z],y=g(b)..G(b),z=f(b,y)..F(b,y),color=gray): bck := plot3d([a,y,z],y=g(a)..G(a),z=f(a,y)..F(a,y),color=yellow): elif IntOrder:-X = 2 then s2 := {x,y}; s1 := {y}; if nops(select(type,indets(ff),name) minus s2)>0 then Do(%MathContainer8 = p1);return;end if; if nops(select(type,indets(FF),name) minus s2)>0 then Do(%MathContainer8 = p2);return;end if; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%MathContainer8 = p3);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%MathContainer8 = p4);return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = p5);return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = p6);return;end if; f := unapply(ff,(x,y)); F := unapply(FF,(x,y)); g := unapply(gg,y); G := unapply(GG,y); bot := plot3d([x,y,f(x,y)],y=a..b,x=g(y)..G(y),color=blue): top := plot3d([x,y,F(x,y)],y=a..b,x=g(y)..G(y),color=red): lft := plot3d([x,a,z],x=g(a)..G(a),z=f(x,a)..F(x,a),color=yellow): rgt := plot3d([x,b,z],x=g(b)..G(b),z=f(x,b)..F(x,b),color=gray): bck := plot3d([g(y),y,z],y=a..b,z=f(g(y),y)..F(g(y),y),color=green): fnt := plot3d([G(y),y,z],y=a..b,z=f(G(y),y)..F(G(y),y),color=gold): elif IntOrder:-X = 3 then s2 := {y,z}; s1 := {z}; if nops(select(type,indets(ff),name) minus s2)>0 then Do(%MathContainer8 = p1);return;end if; if nops(select(type,indets(FF),name) minus s2)>0 then Do(%MathContainer8 = p2);return;end if; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%MathContainer8 = p3);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%MathContainer8 = p4);return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = p5);return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = p6);return;end if; f := unapply(ff,(y,z)); F := unapply(FF,(y,z)); g := unapply(gg,z); G := unapply(GG,z); bot := plot3d([x,y,a],x=f(y,a)..F(y,a),y=g(a)..G(a),color=yellow): top := plot3d([x,y,b],x=f(y,b)..F(y,b),y=g(b)..G(b),color=gray): lft := plot3d([x,g(z),z],z=a..b,x=f(g(z),z)..F(g(z),z),color=green): rgt := plot3d([x,G(z),z],z=a..b,x=f(G(z),z)..F(G(z),z),color=gold): fnt := plot3d([f(y,z),y,z],z=a..b,y=g(z)..G(z),color=blue): bck := plot3d([F(y,z),y,z],z=a..b,y=g(z)..G(z),color=red): elif IntOrder:-X = 4 then s2 := {y,z}; s1 := {y}; if nops(select(type,indets(ff),name) minus s2)>0 then Do(%MathContainer8 = p1);return;end if; if nops(select(type,indets(FF),name) minus s2)>0 then Do(%MathContainer8 = p2);return;end if; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%MathContainer8 = p3);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%MathContainer8 = p4);return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = p5);return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = p6);return;end if; f := unapply(ff,(y,z)); F := unapply(FF,(y,z)); g := unapply(gg,y); G := unapply(GG,y); bot := plot3d([x,y,g(y)],y=a..b,x=f(y,g(y))..F(y,g(y)),color=green): top := plot3d([x,y,G(y)],y=a..b,x=f(y,G(y))..F(y,G(y)),color=gold): lft := plot3d([x,a,z],x=f(a,z)..F(a,z),z=g(a)..G(a),color=yellow): rgt := plot3d([x,b,z],x=f(b,z)..F(b,z),z=g(b)..G(b),color=gray): fnt := plot3d([F(y,z),y,z],y=a..b,z=g(y)..G(y),color=red): bck := plot3d([f(y,z),y,z],y=a..b,z=g(y)..G(y),color=blue): elif IntOrder:-X = 5 then s2 := {x,z}; s1 := {z}; if nops(select(type,indets(ff),name) minus s2)>0 then Do(%MathContainer8 = p1);return;end if; if nops(select(type,indets(FF),name) minus s2)>0 then Do(%MathContainer8 = p2);return;end if; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%MathContainer8 = p3);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%MathContainer8 = p4);return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = p5);return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = p6);return;end if; f := unapply(ff,(x,z)); F := unapply(FF,(x,z)); g := unapply(gg,z); G := unapply(GG,z); bot := plot3d([x,y,a],y=f(x,a)..F(x,a),x=g(a)..G(a),color=yellow): top := plot3d([x,y,b],y=f(x,b)..F(x,b),x=g(b)..G(b),color=gray): lft := plot3d([x,f(x,z),z],z=a..b,x=g(z)..G(z),color=blue): rgt := plot3d([x,F(x,z),z],z=a..b,x=g(z)..G(z),color=red): fnt := plot3d([G(z),y,z],z=a..b,y=f(G(z),z)..F(G(z),z),color=gold): bck := plot3d([g(z),y,z],z=a..b,y=f(g(z),z)..F(g(z),z),color=green): elif IntOrder:-X = 6 then s2 := {x,z}; s1 := {x}; if nops(select(type,indets(ff),name) minus s2)>0 then Do(%MathContainer8 = p1);return;end if; if nops(select(type,indets(FF),name) minus s2)>0 then Do(%MathContainer8 = p2);return;end if; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%MathContainer8 = p3);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%MathContainer8 = p4);return;end if; if not type(evalf(a),numeric) then Do(%MathContainer8 = p5);return;end if; if not type(evalf(b),numeric) then Do(%MathContainer8 = p6);return;end if; f := unapply(ff,(x,z)); F := unapply(FF,(x,z)); g := unapply(gg,x); G := unapply(GG,x); bot := plot3d([x,y,g(x)],x=a..b,y=f(x,g(x))..F(x,g(x)),color=green): top := plot3d([x,y,G(x)],x=a..b,y=f(x,G(x))..F(x,G(x)),color=gold): lft := plot3d([x,f(x,z),z],x=a..b,z=g(x)..G(x),color=blue): rgt := plot3d([x,F(x,z),z],x=a..b,z=g(x)..G(x),color=red): fnt := plot3d([b,y,z],y=f(x,z)..F(b,z),z=g(b)..G(b),color=gray): bck := plot3d([a,y,z],y=f(x,z)..F(a,z),z=g(a)..G(a),color=yellow): else return; end if; P := display([bot,top,lft,rgt,fnt,bck],axes=box,labels=[x,y,z],orientation=[-115,80],style=surface); Do(%Plot0 = P); end module; end use;

use DocumentTools, plots in Do(%Plot0 = display(textplot([0,0," "]),axes=none)); end use;

use DocumentTools, plots in Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); Do(%MathContainer2 = NULL); Do(%MathContainer5 = NULL); Do(%MathContainer3 = NULL); Do(%MathContainer6 = NULL); Do(%MathContainer4 = NULL); Do(%MathContainer7 = NULL); Do(%MathContainer8 = NULL); Do(%Plot0 = display(textplot([0,0," "]),axes=none)); SetProperty(ComboBox0, value, "Select Order"); end use;

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