Chapter 15.1, Problem 37E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the solid that lies under the plane 4*x +* 6*y* − 2*z +* 15 = 0 and above the rectangle *R* = {{*x*, *y*}| −1 ≤ *x* ≤ 2, −1 ≤ *y* ≤ 1}.

To determine

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

Explanation

**Calculation:**

**Formula used:**

The volume of the solid,

**Given:**

The plane is

The rectangular region is,

**Calculation:**

Express the given plane equation as follows:

The volume of the solid is computed as follows.

First, compute the integral with respect to *y*

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