Chapter 15.8, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**24.** Evaluate ∫∫∫_{E}*y*^{2} *dV*, where *E* is the solid hemisphere *x*^{2} + *y*^{2} + *z*^{2}
*y*

To determine

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

Explanation

**Given:**

The function is

The region *B* is hemisphere

**Formula used:**

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

By the given conditions, it is observed that

Use (2) to integrate and apply the limit values

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