Surface integral

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surface integral - urgent please help

Homework Statement


Let S be the surface x=z, x^2+y^2<=1, find ∫∫S(x^2+y^2)dS


Homework Equations


∫∫SFdS = ∫∫S F(ruxrv


The Attempt at a Solution


parametrized surface x=rcostheta y=rsintheta z=rcostheta
i dont know what to do about the partial derivatives regarding x=z did i use the wrong formula? would divergence theorem be better?

the correct answer is sqrt(2)pi/2
 
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Answers and Replies

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LCKurtz
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Homework Statement


Let S be the surface x=z, x^2+y^2<=1, find ∫∫S(x^2+y^2)dS


Homework Equations


∫∫SFdS = ∫∫S F(ruxrv


The Attempt at a Solution


parametrized surface x=rcostheta y=rsintheta z=rcostheta
i dont know what to do about the partial derivatives regarding x=z did i use the wrong formula? would divergence theorem be better?

the correct answer is sqrt(2)pi/2
So you are letting x = x, y = y, z = x and your parameterization is

R(x,y) = <x, y, x>

You can either use Rx X Ry now and substitute the polar equations after, or do the polar substitution now and use RrX Rθ.
 

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