Surface Integral of x^2+y^2 over Parametrized Surface x=z, x^2+y^2<=1

[kthejohn]

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(r_uxr_v

The Attempt at a Solution

parametrized surface x=rcostheta y=rsintheta z=rcostheta
i don't 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

 

[LCKurtz]

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(r_uxr_v

The Attempt at a Solution

parametrized surface x=rcostheta y=rsintheta z=rcostheta
i don't 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 R_x X R_y now and substitute the polar equations after, or do the polar substitution now and use R_rX R_θ.