Chapter 15.8, Problem 22E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**22.** Evaluate ∫∫∫_{E}*y*^{2}*z*^{2} *dV*, where *E* lies above the cone
*ρ* = 1.

To determine

**To evaluate:** The given triple integral by using spherical coordinates.

Explanation

**Given:**

The function is

The region *E* lies above the cone

**Formula used:**

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

By the given conditions, it is observed that

Use the formula mentioned above to change the given problem into spherical coordinates. Then, by the equation (1), the value of the given triple integral is,

Use the equation (2) to integrate and apply the limit values

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