1. Surface Integral help

Hey, really stuck on this question.

Integrate

$\displaystyle f(x,y,z)= \sqrt{3x^2+3y^2+z+1}$

over the surface given by the graph $\displaystyle z=g(x,y)=x^2+y^2$ over the region $\displaystyle 1<x^2+y^2<4$.

I did some working but it got far too complicated for the integral.

Any help would be very nice.

Thanks

2. Originally Posted by Nguyen
Hey, really stuck on this question.

Integrate

$\displaystyle f(x,y,z)= \sqrt{3x^2+3y^2+z+1}$

over the surface given by the graph $\displaystyle z=g(x,y)=x^2+y^2$ over the region $\displaystyle 1<x^2+y^2<4$.

I did some working but it got far too complicated for the integral.

Any help would be very nice.

Thanks
first note that and covert to cylindrical coordinates to get

$\displaystyle dS=\sqrt{\left( \frac{\partial z}{\partial x} \right)^2+\left( \frac{\partial z}{\partial y} \right)^2 +1}=\sqrt{2}dA$

$\displaystyle \int_{0}^{2\pi}\int_{1}^{2}\sqrt{3(r^2)+r^2+1}rdrd \theta$

$\displaystyle \int_{0}^{2\pi}\int_{1}^{2}\sqrt{4r^2+1}rdrd\theta$

3. oh yes, thanks TheEmptySet, I see where my thinking was wrong. And thanks for the very fast reply!