Chapter 14, Problem 52RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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 âˆ«03âˆ«Ï€2Ï€âˆ«25zsinxdydxdz.

Formula used:

Integration formula:

âˆ«abxndx=[xn+1n+1]ab

âˆ«basinxdx=[âˆ’cosx]ba

Calculation:

Consider the givenintegral:

âˆ«03âˆ«Ï€2Ï€âˆ«25zsinxdydxdz

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

âˆ«03âˆ«Ï€2Ï€âˆ«25zsinxdydxdz=âˆ«03âˆ«Ï€2Ï€[yzsinx]25dxdz=âˆ«03

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