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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find the volume of the solid enclosed by the surface z = x2 + xy2 and the planes z = 0, x = 0, x = 5, and y = ±2.

To determine

To find: The volume of the solid that enclosed by the surface and the planes.

Explanation

Calculation:

Formula used:

The volume of the solid, V=RzdA , where, z is the given function.

Given:

The surface is z=x2+xy2 .

The planes are z=0,x=0,x=5 and y=±2 .

Calculation:

Consider the rectangular region as R=[0,5]×[2,2] .

Then , the volume of the solid is computed as follows.

V=RzdA=0522(x2+xy2)dydx

First, compute the integral with respect to y.

V=05[x2y+xy33]22dx

Apply the limit value for y,

V=05<

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Chapter 15 Solutions

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