Chapter 16.9, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the Divergence Theorem to evaluate
*S* is the sphere *x*^{2} + *y*^{2} + *z*^{2} = 1.

To determine

**To evaluate:** The integral

Explanation

**Given Data:**

Write the given integral as follows.

Here,

Write the given equation of the sphere as follows.

**Formula used:**

Write the expression to find flux of the vector field

Write the expression to find

Here,

Write the expression to find divergence of vector field

Write the expression to find volume of the sphere with the radius

From equation (1) and (2), it is clear that the expression

For the surface

As the surface is a sphere with the equation

If the normal

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