Chapter 16.8, Problem 5E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

**F**(*x*, *y, z*) = *xyz* **i** + *xy* **j** + *x*^{2}*yz* **k**. *S* consists of the top and the four sides (but not the bottom) of the cube with vertices (±1, ±1, ± 1), oriented outward

To determine

**To evaluate**: The expression

Explanation

**Given data:**

Consider the expression for the vector field

And *S* is the cube with vertices

**Formula Used:**

Consider the expression for the Stokesâ€™ theorem,

Consider *C* is the square in the plane

Consider
*C* and both surfaces satisfy the hypotheses of Stokes' Theorem. Therefore, consider the following expression.

Calculate

For the surface
*C* has the same orientation for both surfaces

Calculate

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P-6RECh-16 P-7RECh-16 P-8RECh-16 P-9RECh-16 P-10RECh-16 P-11RECh-16 P-12RECh-16 P-13RECh-16 P-14RECh-16 P-15RECh-16 P-16RECh-16 P-17RECh-16 P-18RECh-16 P-19RECh-16 P-20RECh-16 P-21RECh-16 P-22RECh-16 P-23RECh-16 P-24RECh-16 P-25RECh-16 P-27RECh-16 P-28RECh-16 P-29RECh-16 P-30RECh-16 P-31RECh-16 P-32RECh-16 P-33RECh-16 P-34RECh-16 P-35RECh-16 P-36RECh-16 P-37RECh-16 P-38RECh-16 P-39RECh-16 P-40RECh-16 P-41RECh-16 P-1PCh-16 P-2PCh-16 P-3PCh-16 P-5PCh-16 P-6P

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