   Chapter 14.6, Problem 10E

Chapter
Section
Textbook Problem

Evaluating a Triple Iterated Integral In Exercises 3-10, evaluate the triple iterated integral. ∫ 0 π / 2 ∫ 0 y / 2 ∫ 0 1 / y sin y   d z   d x   d y

To determine

To calculate: The value of triple iterated integral 0π20y201ysinydzdxdy.

Explanation

Given:

The triple iterated integral 0π20y201ysinydzdxdy.

Formula used:

sinxdx=cosx

And,

amda=am+1m+1

Where a is a variable and m is a scalar value.

Calculation:

Here, the first integration is performed with respect to z, so the variables x and y are treated to be

constant.

So,

0π20y201ysinydzdxdy=0π20y2[sinyz]01ydxdy=0π20y2(siny(1y0))d

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