Chapter 15.2, Problem 26E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**26.** Enclosed by the paraboloid *z* = *x*^{2} + *y*^{2} + 1 and the planes *x* = 0, *y* = 0, *z* = 0, and *x* + *y* = 2

To determine

**To find:** The volume of the solid that enclosed by the paraboloid and the planes*.*

Explanation

**Given:**

The paraboloid is

The planes are,

**Formula used:**

The volume of the solid,

**Calculation:**

The plane equation can be modified as
*y* varies from 0 to
*x* varies from 0 to 2. Thus, the volume of the solid is computed as follows.

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

Apply the limit value for *y*,

Compute the integral with respect to *x*

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