   Chapter 15.2, Problem 24E

Chapter
Section
Textbook Problem

Find the volume of the given solid.24. Under the surface z = 1+ x2y2 and above the region enclosed by x = y2 and x = 4

To determine

To find: The volume of the solid that lies under the surface and above the region D.

Explanation

Given:

The surface is z=1+x2y2 .

The region D is, x=4,x=y2 .

Formula used:

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

Calculation:

Solve both the equation of the region D and obtain y = −2 and 2. Thus, the volume of the solid is computed as follows.

V=RzdA=22y24(1+x2y2)dxdy

First, compute the integral with respect to x.

V=22[x+x3y23]y24dy

Apply the limit value for x,

V=22[(4+(4)3y23)(y2+(y2)3y23)]dy=22[4+61y23y83]dy

Compute the integral with respect to y

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