Chapter 16.9, Problem 31E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Suppose *S* and *E* satisfy the conditions of the Divergence Theorem and *f* is a scalar function with continuous partial derivatives. Prove that
*Hint:* Start by applying the Divergence Theorem to F = *f*c, where c is an arbitrary constant vector.]

To determine

**To prove:** The expression

Explanation

**Given Data:**

The regions

The given expression that has to be proved is

**Formula used:**

The expression to find flux of the vector field

The expression to find divergence of vector field

**Calculation:**

Consider an arbitrary constant vector

Consider the vector field

Substitute

Substitute

Substitute

If

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