Chapter 16.8, Problem 20E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Suppose *S* and *C* satisfy the hypotheses of Stokes’ Theorem and *f, g* have continuous second-order partial derivatives. Use Exercises 24 and 26 in Section 16.5 to show the following.

(a) ∫* _{c}*(

(b) ∫* _{c}*(

(c) ∫* _{c}* (

**(a)**

To determine

**To show**: The expression

Explanation

**Given data:**

Consider *S* and *C* satisfy the hypotheses of Stokesâ€™ Theorem, *f* and *g* have continuous second-order partial derivatives.

Consider the following expressions from Exercises 24 and 26 in section 16.5.

**Formula used:**

Write the expression for the Stokesâ€™ theorem.

Write the expression for

**(b)**

To determine

**To show**: The expression

**(c)**

To determine

**To show**: The expression

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