Basically trying to calculate the surface integral of the top surface described by the equation: $x^2 + y^2 = 9$ as the outside cylinder with the top defined by $x + z = 5$ - a nice and simple integral $\int yzds$. My understanding for the top surface is to take x and y as parameters, (meaning z = 5 - x), which you can then use to get the integral $\int xz \sqrt{2} dxdy$ Which can then be converted into polar co-ordinates to solve. This is where my problem comes in - there's a z? With drd$\theta$, I can't convert the z. If you convert that into x-5, the resulting integral is a mess and I can't solve it. I've attached my working so far beneath:
Any ideas where I went wrong or which direction I should go?
Thanks in advance!
