Find the flux of F across the surface sigma by expressing sigma parametrically.
F(x,y,z)=xi+yj+zk; sigma is the portion of the cylinder x^2+z^2=1 between the planes y=1 and y=-2, oriented by outward unit normals.
Find the flux of F across the surface sigma by expressing sigma parametrically.
F(x,y,z)=xi+yj+zk; sigma is the portion of the cylinder x^2+z^2=1 between the planes y=1 and y=-2, oriented by outward unit normals.
Parametrize the given surface as and . So we have the limits as and .
The surface is now .
To calculate the normal to the surface, we have, .
.
The flux is now calculated as
Could you substitute and complete this?
The term
has to be in the same dirction os the orientation vector n . since n is outward we would use [cos(theta),0, sin(theta)]
Also the outer limit of integration shoud be -2 to 1
Of course these cancel and you would have the correct answer --if thats what you had in mind I apologize for my remarks.