   Chapter 14, Problem 52RE

Chapter
Section
Textbook Problem

Evaluating a Triple Iterated IntegralIn Exercises 49–52, evaluate the triple iterated integral. ∫ 0 3 ∫ π / 2 π ∫ 2 5 z sin x   ​ d y   d x   d z

To determine

To calculate: The value of the integral 03π2π25zsinxdydxdz with triple iterated.

Explanation

Given:

The triple iterated integral is 03π2π25zsinxdydxdz.

Formula used:

Integration formula:

abxndx=[xn+1n+1]ab

basinxdx=[cosx]ba

Calculation:

Consider the givenintegral:

03π2π25zsinxdydxdz

Assume remaining variable constant andintegrate the provided expression with respect to y,

03π2π25zsinxdydxdz=03π2π[yzsinx]25dxdz=03

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