Chapter 16.7, Problem 3E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Let *H* be the hemisphere *x*^{2} + *y*^{2} +* z*^{2} = 50, *z* ⩾ 0, and suppose *f* is a continuous function with *f*(3, 4, 5) = 7, *f*(3, −4, 5) = 8, *f*(−3, 4, 5) = 9, and *f*(−3, −4, 5) = 12. By dividing *H* into four patches, estimate the value of ∬* _{H} f*(

To determine

**To find:** The value of

Explanation

**Given data:**

*H* be the hemisphere

The *xz*- and *yz*- planes are used to divide hemisphere

Therefore,

The sample points in the four patches are

Find

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