Chapter 16, Problem 29RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the surface integral.

**29.** ∬_{S}**F** · *d*S, where **F**(*x*, *y*, *z)* = *xz* **i** − 2*y* **j** + 3*x* **k** and *S* is the sphere *x*^{2} + *y*^{2} + *z*^{2} = 4 with outward orientation

To determine

**To Evaluate:** The surface integral of

Explanation

**Given data:**

**Formula used:**

Write the expression for Divergence Theorem.

Write the expression for volume of sphere.

Write the expression for divergence.

Consider the expression as follows.

Write the expression for sphere.

Compare equations (4) and (5).

Consider the expression for

Write the expression for

Compare equations (6) and (7)

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