Find the flux ofFacross 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.

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- Apr 23rd 2009, 07:43 PMnoles2188Flux
Find the flux of

**F**across the surface sigma by expressing sigma parametrically.

**F**(x,y,z)=x**i**+y**j**+z**k**; 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. - Apr 23rd 2009, 11:58 PMchainruleQuote:

Find the flux of**F**across the surface sigma by expressing sigma parametrically.

**F**(x,y,z)=x**i**+y**j**+z**k**; 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? - Apr 24th 2009, 01:16 AMCalculus26
The term http://www.mathhelpforum.com/math-he...19ca2c57-1.gif

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.