Originally Posted by

**Silverflow** Hi all,

I've been given a question based on Stoke's Theorem, and the question is as follows:

Given the surface, $\displaystyle S=x^2+y^2+2(z-1)^2=6, z\geq0$ and the vector field $\displaystyle \underline{F}=(xz-y^3cos(z))\underline{i}+(x^3e^z)\underline{j}+(xyz e^{x^2+y^2+z^2})\underline{k}$. Use stokes formula to evaluate the integral$\displaystyle \int\int_{S}curl\underline{F}.\underline{S}$.

My answer:

Using Stokes Theorem: $\displaystyle \int\int_{S}curl\underline{F}.d\underline{S}=\int_ {C}\underline{F}.d\underline{r}$.

So, I need to find $\displaystyle d\underline{r}$. I can find a vector equation for S:

$\displaystyle \underline{r}(t)=2cos(t)\underline{i}+2sin(t)\unde rline{j}+2\underline{z}$.

Then, I can calculate $\displaystyle \underline{r}'(t)$ & $\displaystyle \underline{f}(\underline{r}(t))$. However, the latter leaves me with something that looks hideously ugly. I was just wondering if any could go over this, see whether I've done the right thing.

Thank you in advance!