   Chapter 16.7, Problem 4E

Chapter
Section
Textbook Problem

Suppose that f(x, y, z) = g( ), where g is a function of one variable such that g(2) = −5. Evaluate ∬S f(x, y, z) dS, where S is the sphere x2 + y2 + z2 = 4.

To determine

To find: The value of Sf(x,y,z)dS .

Explanation

Given data:

S be the sphere x2+y2+z2=4 ,

f(x,y,z)=g(x2+y2+z2) and g(2)=5 .

The total and surface area of a sphere (SdS) is 4πr2 .

Find Sf(x,y,z)dS .

Sf(x,y,z)dSSg(x2+y2+z2)dSSg(2)dS

Substitute –5 for g(2) ,

Sf(x,y,z)

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