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kevinf

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hi in my engineering mathematics class, we are going over surface integrals again. i have some general question about this subject. sorry for not using the template.

say that i have a problem that goes like this.

"evaluate [tex]\int(v*dS)[/tex] (where the * means dot) where v= (3y,2x[tex]^{2}[/tex],z[tex]^{3}[/tex]) and S is the surface of the cylinder x[tex]^{2}[/tex] + y[tex]^{2}[/tex]=1, 0<z<1. "

to find dS, is it always the unit vector of z=6-2x-2y (gradient of z divide by magnitude of z) multiply by dx and dy? i am not sure if i am right on the dx and dy though.

also some of the problems' solutions use cylindrical coordinates, which i understand, but some of them only use r d[tex]\varphi[/tex] dz. if i remember correclty from my calculus classes, i thought the cylindrical coordinates also included dr?

say that i have a problem that goes like this.

"evaluate [tex]\int(v*dS)[/tex] (where the * means dot) where v= (3y,2x[tex]^{2}[/tex],z[tex]^{3}[/tex]) and S is the surface of the cylinder x[tex]^{2}[/tex] + y[tex]^{2}[/tex]=1, 0<z<1. "

to find dS, is it always the unit vector of z=6-2x-2y (gradient of z divide by magnitude of z) multiply by dx and dy? i am not sure if i am right on the dx and dy though.

also some of the problems' solutions use cylindrical coordinates, which i understand, but some of them only use r d[tex]\varphi[/tex] dz. if i remember correclty from my calculus classes, i thought the cylindrical coordinates also included dr?

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