Originally Posted by

**caliber** Hi People

New here, so please be kind!

I am doing some work for my maths module, I have got so far but I am not sure if it is correct, and if not, why not. It is important to me to getting it correct because this will also be on my exam so any help you can give me will be very much appreciated.

Thanks in advance!

The question:

Region V of a cylinder is denoted by $\displaystyle x^2+y^2\leq 1, 0 \leq z \leq 2$ and S is the surface of this cylinder.

Vector field $\displaystyle F(x,y,z) = xi + yi + z(x^2+y^2)k$

Now, I have been instructed earlier in the question to convert F into cylindrical co-ordinates, so...

$\displaystyle F(\rho,\varphi,z) = \rho \widehat{\rho} + z\rho^{2}\widehat{z}$

I am then instructed to find the surface integral. I do this, but am unable to do it in cylindrical co-ordinates. Is this correct?

I have a feeling it is not, because at the end of it I am left with an answer simply of 8pi

Once again, thanks for any help and if you need any more workings and such I can provide them.