Chapter 15.6, Problem 25E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the Midpoint Rule for triple integrals (Exercise 24) to estimate the value of the integral. Divide *B* into eight sub-boxes of equal size.

**25**.

To determine

**To estimate:** The value of the integral by using the Midpoint Rule for triple integral and also divide the region *B* into 8 sub-boxes of equal size.

Explanation

**Given:**

The integral is

The region is

**Rule used:** Midpoint Rule for triple integral

The triple integral of *f* over the box is, if the limit exists then,

**Calculation:**

To find the volume of each sub-box , each interval of *x,y,z* must be divided by 2. Therefore,

Now find the midpoint of each sub-box is

Here divide the region *B* into 8 sub-boxes with equal sides

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