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- #1

Please doublecheck my work, and let me know if where I am stuck is correct, or if I am on the completely wrong path.

Evaluate the surface integral \(\int\int f(x,y,z)dS\) using an explicit representation of the surface.

\(f(x,y,z) = x^2 + y^2;\mbox{ S is the paraboloid } z= x^2 + y^2\mbox{ for }0\leq z \leq 4\)

\(dS=\sqrt{4x^2+4y^2+1}\)

\(\int\int(x^2+y^2)*2*\sqrt{x^2+y^2+\frac{1}{4}}dA\)

\(\int_0^{2\pi}\int_0^4(r^2)*(r^2+\frac{1}{4})^{1/2}dzrdr\)

It's late, I'm not thinking straight. I'm sure that this should be integrated with respect to dxdy, not dzrdr, but it isn't clicking right.

A point in the right direction would be appreciated.

Thanks,

Mac