Chapter 15, Problem 48RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates to evaluate

To determine

**To evaluate:** The integral by changing to spherical coordinates.

Explanation

**Formula used:**

If *E* given by

If *z* then,

The spherical coordinates

**Given:**

The function is

The rectangular coordinates of the given triple integral are

**Calculation:**

Substitute

The limits become,

And

On simplifying further, this equation becomes,

From the equations above, it is observed that the region lies above the cylinder and below the sphere with center at origin. Thus, by the equation (1), the integral becomes,

Apply the equation (2) to separate the integrals

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