Chapter 16.7, Problem 26E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the surface integral ∫∫* _{s}* F ·

**26. F**(*x*, *y, z*) = *y* **i** - *x* **j** + 2*z* **k,** *S* is the hemisphere *x*^{2} *+ y*^{2} *+ z*^{2}* = 4, z* ≥ 0*,* oriented downward

To determine

**To find:** The value of

Explanation

**Given data:**

**Formula used:**

Rearrange equation (2).

Consider

Substitute

The *D* is disk
*S* has downward orientation, modify equation (3).

Substitute

Substitute

Let

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