Methods of Integration Trig Substitution JSFH
<Text-field style="Heading 1" layout="Heading 1">Problem 4-7</Text-field> JSFH Evaluate the integral 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 by making the trig substitution 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.
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<Text-field style="Heading 1" layout="Heading 1">Evaluate the Indefinite Integral</Text-field> JSFH Control-drag the integral. Context Menu: Evaluate and Display Inline LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFHJSFH
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<Text-field style="Heading 1" layout="Heading 1">Mathematical Solution</Text-field> JSFH 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 JSFH 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 JSFH 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 JSFH 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 JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRzaW5GJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZSRjlGOUY5Rjk= JSFH 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Fjr JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Solution by Tutor</Text-field> JSFH Tools: Load Package\342\211\273Student Calculus 1 JSFH Control-drag the integral Context Menu: 2-D Math\342\211\273Convert To\342\211\273Inert Form Context Menu: Tutors\342\211\273Integration Methods Change: 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 Change: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRzaW5GJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZSRjlGOUY5Rjk= Constant Multiple Power rule Revert (twice) JSFH JSFH JSFH JSFH JSFH JSFH JSFH
Student[Calculus1][IntTutor](); JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution from First Principles</Text-field> JSFH Enter the integrand and press the Enter key. Context Menu: Evaluate at a Point\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVy1GLDYlUSR0YW5GJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZmbkY5RjlGOUY5 JSFH eval( , [x = 2*tan(t)]); JSFH JSFH Multiply this result by the derivative of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSR0YW5GJy8lJ2l0YWxpY0dGOEYvLUkobWZlbmNlZEdGJDYkLUYjNiQtRks2JVEnJiM5NTI7RidGTkYvRi9GLy1GSzYjUSFGJ0Yv, namely, by 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 Press the Enter key. Context Menu: Simplify\342\211\273Symbolic Context Menu: Constructions\342\211\273Integral\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFHJSFH Make the substitution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRzaW5GJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZSRjlGOUY5Rjk= Tools\342\211\273Tasks\342\211\273Browse: Calculus - Integral\342\211\273Methods of Integration\342\211\273Substitution
Integration by Substitution Enter the integral 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: JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkSW50RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUkobWFjdGlvbkdGJDYkLUYjNigtRiw2I1EhRictRiM2KUY9LUYjNiUtSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JlEiMUYnLyUrZm9yZWdyb3VuZEdRK1s5NSwwLDIxN11GJy8lMGZvbnRfc3R5bGVfbmFtZUdROE1hcGxlfklucHV0flBsYWNlaG9sZGVyRicvRjNRJ25vcm1hbEYnLUYjNiUtSSZtc3FydEdGJDYjLUYjNictRkg2JlEiNEYnRktGTkZRLUkjbW9HRiQ2L1EqJnVtaW51czA7RidGS0ZORlEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRl1vLyUpc3RyZXRjaHlHRl1vLyUqc3ltbWV0cmljR0Zdby8lKGxhcmdlb3BHRl1vLyUubW92YWJsZWxpbWl0c0dGXW8vJSdhY2NlbnRHRl1vLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGXHAtSSVtc3VwR0YkNiUtRiw2J1EieEYnRi9GS0ZORjItRiM2JS1GSDYmUSIyRidGS0ZORlEvJStleGVjdXRhYmxlR0Zdb0ZRLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZqcEZRRmpwRlEvJS5saW5ldGhpY2tuZXNzR0ZKLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmNxLyUpYmV2ZWxsZWRHRl1vRmpwRlEtRmhuNi9RIixGJ0ZLRk5GUUZbby9GX29GMUZgb0Zib0Zkb0Zmb0Zoby9GW3BRJjAuMGVtRicvRl5wUSwwLjMzMzMzMzNlbUYnLUYjNiVGYnBGanBGUUY9RmpwRlFGPUZqcC8lLHBsYWNlaG9sZGVyR0YxRlEvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0OnRhc2stcGxhY2Vob2xkZXJGJ0ZRRj1GanBGUQ== Define the substitution: 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 Transform the integral: 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
JSFH Reference transformed integral by equation label. Press the Enter key. Context Menu: Evaluate (from Inert) Context Menu: Evaluate at a Point\342\211\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 JSFH eval( , [u = sin(arctan(x/2))]); JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH
JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH