Chapter 15.2, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**23.** Under the plane 3*x* + 2*y* – *z* = 0 and above the region enclosed by the parabolas *y* = *x*^{2} and *x* = *y*^{2}

To determine

**To find:** The volume of the solid that lies under the plane and above the region enclosed by parabolas.

Explanation

**Given:**

The plane is

The parabolas are,

**Formula used:**

The volume of the solid,

**Calculation:**

Express the given plane equation as follows:

The parabola

Solve both the equation of the parabola and obtain the limit for *x* as 0 to 1.

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

First, compute the integral with respect to *y*.

Apply the limit value for *y*,

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