   Chapter 15.2, Problem 37E

Chapter
Section
Textbook Problem

Find the volume of the solid by subtracting two volumes.37. The solid under the plane z = 3, above the plane z = y, and between the parabolic cylinders y = x2 and y = 1 − x2

To determine

To find: The volume of the solid that lies in between two planes.

Explanation

Given:

The planes are z=3,z=y .

The parabolic cylinders are, y=x2,y=1x2 .

Formula used:

The volume of the solid, V=Dz1dADz2dA , where, z1 and z2 are the given function.

Calculation:

Express the given plane equation as follows:

z1=3

And, z2=y .

The parabolas intersect at x=12 and 12 . Therefore, x varies from - 12 and 12 and y varies from x2 to 1x2 .

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

First, compute the integral with respect to y

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