   Chapter 15, Problem 7RE

Chapter
Section
Textbook Problem

Calculate the iterated integral.7. ∫ 0 π ∫ 0 1 ∫ 0 1   −   y 2 y   sin x   d z   d y   d x

To determine

To calculate: The value of given iterated integral.

Explanation

Calculation:

First, compute the integral with respect to z.

0π0101y2ysinxdzdydx=0π01[01y2ysinxdz]dydx=0π01[yzsinx]01y2dydx

Apply the limit values for z.

0π0101y2ysinxdzdydx=0π01[y(1y2)sinxy(0)sinx]dydx=0π01[ysinx1y20]dydx=0π01[ysinx1y2]dydx=0π[01ysinx1y2dy]dx

Compute the integral with respect to y. For that substitute t=y2,dt=2ydy

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