   Chapter 15.7, Problem 14E ### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

#### Solutions

Chapter
Section ### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Using the Divergence Theorem In Exercises 9-18, use the Divergence Theorem to evaluate ∫ S ∫ F ⋅ N   d S and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results. F ( x , y , z ) = x y z j S: x 2 + y 2 = 4 , z = 0 , z = 5

To determine

To calculate: The value of SFNdS by the divergence theorem.

Explanation

Given:

The vector field, F(x,y,z)=xyzj, S: x2+y2=4, z=0, z=5.

Formula used:

The divergence theorem, SFNdS=QdivFdV

Calculation:

Find the divergence of vector field F,

·F=·(xyzj)=(xi+yj+zk).(xyzj)=y(xyz)=xz

For the surface bounded by S: x2+y2=4, a cylinder of radius, r = 2, and height 0z5

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