Chapter 15, Problem 7RCC

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Write the definition of the triple integral of *f* over a rectangular box *B.*

(b) How do you evaluate

(c) How do you define
*E* is a bounded solid region that is not a box?

(d) What is a type 1 solid region? How do you evaluate
*E* is such a region?

(e) What is a type 2 solid region? How do you evaluate
*E* is such a region?

(f) What is a type 3 solid region? How do you evaluate
*E* is such a region?

(a)

To determine

**To write:** The definition of the triple integral of *f* over a given rectangular box *B*.

Explanation

The triple integral of *f* is defined using the Riemann sum for the three dimensional space. It is given by,

(b)

To determine

**To evaluate:** The given integral

(c)

To determine

**To define:**
*E* is a bounded region.

(d)

To determine

**To explain:** The type 1 region and the method of evaluating it.

(e)

To determine

**To explain:** The type 2 region and the method of evaluating it.

(f)

To determine

**To explain:** The type 3 region and the method of evaluating it.

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