   Chapter 14.7, Problem 14E

Chapter
Section
Textbook Problem

Volume In Exercises 11-14, sketch the solid region whose volume is given by the iterated integral and evaluate the iterated integral. ∫ 0 2 π ∫ 0 π ∫ 2 5 ρ 2 sin   ϕ   d ρ   d ϕ   d θ

To determine

To graph: The solid region whose volume is given by iterated integral 02π0π25ρ2sinϕdρdϕdθ and to evaluate the integral.

Explanation

Given: 02π0π25ρ2sinϕdρdϕdθ

Graph:

To sketch the solid region with the help of maple follow these commands:

>plot3d([2,5],ϕ=0..π,θ=0..2π,coords=spherical,coords = spherical, transparency = 0.5, labels = [r,θ,ϕ])

Therefore, the sketch is drawn as shown below:

Calculation:

Consider the provided integral,

02π0π25ρ2sinϕdρdϕdθ

From this,

I=02π

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