   Chapter 14.7, Problem 6E

Chapter
Section
Textbook Problem

Evaluating a Triple Iterated IntegralIn Exercises 3–8, evaluate the triple iterated integral. ∫ 0 π / 2 ∫ 0 π ∫ 0 2 e − p 3 p 2   d p   d θ   d ϕ

To determine

To calculate: The triple integral 0π20π02eρ3ρ2dρdθdϕ

Explanation

Given:

The triple integral, 0π20π02eρ3ρ2dρdθdϕ

Calculation:

Consider the integral,

0π20π02eρ3ρ2dρdθdϕ

Let, ρ3=u.

Then,

3ρ2dρ=duρ2dρ=du3

And, the limits are 0 to 8.

Substitute the values in the above integral, to get,

0π20π02eρ3ρ2dρdθdϕ=130π20π08eududθdϕ=13

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