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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Evaluate the iterated integral.

4. 0 π / 2 0 x x sin y d y d x

To determine

To estimate: The value of given iterated integral.

Explanation

Compute the value of the iterated integral as shown below.

0π20x(xsiny)dydx=0π2[0x(xsiny)dy]dx=0π2[(xcosy)]0xdx=0π2(xcosx+x)dx=0π2xdx0π2xcosxdx

To integrate the second term, use integration by parts.

Let u=x and dv=cosxdx .

Then, dv=cosxdx

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Chapter 15 Solutions

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