Chapter 15.2, Problem 37E

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8th Edition

James Stewart

ISBN: 9781285741550

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* = *x*^{2} and *y* = 1 − *x*^{2}

To determine

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

Explanation

**Given:**

The planes are

The parabolic cylinders are,

**Formula used:**

The volume of the solid,

**Calculation:**

Express the given plane equation as follows:

And,

The parabolas intersect at
*x* varies from *-*
*y* varies from

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

First, compute the integral with respect to *y*

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