Divergence theorem with inequality

Homework Statement

F(x,y,z)=4x i - 2y^2 j +z^2 k

S is the cylinder x^2+y^2<=4, The plane 0<=z<=6-x-y

Find the flux of F

The Attempt at a Solution

What is the difference after if I change the equation to inequality?

For example :
x^2+y^2<=4, z=0

x^2+y^2<=4 , z=6-x-y

x^2+y^2=4, z=6-x-y

thanks!

Last edited:

member 587159

Homework Statement

F(x,y,z)=4x i - 2y^2 j +z^2 k

S is the cylinder x^2+y^2=4, 0<=z<=3

The Attempt at a Solution

[/B]
I find that the answer is 84 pi

What is the difference after if I change the equation to inequality?

For example :
x^2+y^2<=4, z=3

x^2+y^2<=4 , z=0

X^2+y^2=4, z=3

thanks!

Make a sketch and everything will become clear.

LCKurtz
Homework Helper
Gold Member

Homework Statement

F(x,y,z)=4x i - 2y^2 j +z^2 k

S is the cylinder x^2+y^2=4, 0<=z<=3

The Attempt at a Solution

[/B]
I find that the answer is 84 pi

What is the difference after if I change the equation to inequality?

For example :
x^2+y^2<=4, z=3

x^2+y^2<=4 , z=0

X^2+y^2=4, z=3

thanks!

One inequality gives the surface of the cylinder and the other gives the solid cylinder.

Sorry, I made some mistake previously and I modified the question.
If I want to find the flux of the bottom face, top face, side surface of cylinder and the tangent surface of the cylinder,
How can I express it in inequality?

LCKurtz