Chapter 15.1, Problem 43E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid enclosed by the paraboloid *z =* 2 + *x*^{2} + (y − 2)^{2} and the planes *z* = 1, *x* = 1, *x* = −1, *y* = 0, and *y* = 4.

To determine

**To find:** The volume of the solid in the first octant bounded by the cylinder.

Explanation

**Formula used:**

The volume of the solid,

**Given:**

The surface is

The planes are

**Calculation:**

The rectangular region is

Therefore, the volume of the solid is obtained as follows.

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

Apply the limit value for *y*,

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