Chapter 15.8, Problem 41E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the integral by changing to spherical coordinates.

**41.**
* xy dz dy dx*

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,

Solve the equation and obtain

From the equations above, it is observed that the region lies above the cone and below the sphere of radius

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