   Chapter 15.2, Problem 4E

Chapter
Section
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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