Riemann Sum Iterated Double Integral JSFH
<Text-field style="Heading 1" layout="Heading 1">Problem 5-7</Text-field> JSFH Using a Riemann sum, approximate the iterated integral 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 .
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution by Tutor</Text-field> JSFH Tools\342\211\273Load Package: Student Multivariate Calculus JSFH Control-drag the integral. Context Menu: 2-D Math\342\211\273Convert To\342\211\273Inert Form Context Menu: Tutors\342\211\273Approximate Integration JSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution from First Principles</Text-field> JSFH Enter the integrand as a function Enter the equation 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. Context Menu: Assign Function. JSFH Define stepsizes 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 and 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 Type 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 Context Menu: Assign to a Name\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= JSFH Type 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 Context Menu: Assign to a Name\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= JSFH Form the iterated sum Expression palette: Summation template Create the iterated sum 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 Context Menu: 2-D Math\342\211\273Convert To\342\211\273Inert Form Context Menu: Assign to a Name\342\211\273DoubleSum JSFH Write and evaluate the iterated limit Expression palette: limit operator Enter the expression 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 Context Menu: Evaluate and Display Inline JSFH
JSFH
JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH