Chapter 15.1, Problem 39E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid lying under the elliptic paraboloid *x*^{2}*/*4 + *y*^{2}*/*9 + *z* = 1 and above the rectangle *R* = [−1, 1] × [−2, 2].

To determine

**To find:** The volume of the solid that lies under the elliptic paraboloid and above the rectangular region.

Explanation

**Calculation:**

**Formula used:**

The volume of the solid,

Here,

**Given:**

The elliptic paraboloid is

The rectangular region is,

**Calculation:**

Express the elliptic paraboloid as

The volume of the solid is computed as follows.

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

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