
Surface Integrals
Evaluate the following. (Give an exact answer.)
Question is
$\displaystyle \iint\limits_{S} f(x,y,z) \, dS$
f(x,y,z)= $\displaystyle \sqrt{x^2+y^2+z^2}$
$\displaystyle S: z=\sqrt{x^2+y^2}~,(x1)^2+y^2\le1$
So after some work i arrive to to this.
$\displaystyle \sqrt{2}\int_0^2\int_{\sqrt{1(x1)^2}}^{\sqrt{1(x1)^2}}\sqrt{x^2+y^2}\,dy\,dx$
which i then turn into sperical and get
$\displaystyle \sqrt{2}$ $\displaystyle \int_0^{\frac{2}{\pi}}\int_0^1~r^2\,dr\,d\theta$ which equals $\displaystyle 2\pi\frac{\sqrt{2}}{3}$
But my book example has a similar question as
$\displaystyle 2$ $\displaystyle \int_0^{\frac{2}{\pi}}\int_0^1~r^2\,dr\,d\theta$ which equals $\displaystyle \frac{4\pi}{3}$
Which is right? Why is theirs 2 and mine $\displaystyle \sqrt{2}$ and are my limits right? Or is it all wrong :( Thanks for the help.

Re: Surface Integrals
Hey tastylick.
It might have something to do with the Jacobian: did you calculate this and if so what did you get?

1 Attachment(s)
Re: Surface Integrals
Attachment 29734
My work is attached.