Stokes’ Theorem to find integration Use Stokes’ Theorem to evaluate integration $c (xy \,dx+ yz\, dy + zx\, dz)$ where and $C$ is the triangle with vertices $(1,0,0),(0,1,0),(0,0,1)$, oriented counter-clockwise rotation as viewed from above.
can anyone please help me with this?

You are planning to evaluate the path integral
$$\oint_C \vec{X} \cdot d\vec{r}$$
where
$$\vec{X} = \left(\begin{array}{cc}xy\\yz\\zx\end{array}\right) \ .$$
Stokes Theorem gives
$$\oint_C \vec{X} \cdot d\vec{r} = \iint_{\text{Inside} \ C} \nabla\times \vec{X} \cdot d\vec{S}$$
so we start by evaluating (google how to compute a curl) 
$$\nabla \times \vec{X} = \left(\begin{array}{c}-y\\-z\\-x\end{array}\right) \ .$$
Fortunately, the curl is quite simple. What´s left is evaluating
$$-\iint_{\text{Inside} \ C} \left(\begin{array}{c}y\\z\\x\end{array}\right) \cdot d\vec{S} \ .$$
Now find a two-dimensional parametrisation of the surface that is the inside of triangle C and use the standard procedure to solve the surface integral. Definitely make a 3D-sketch to avoid errors. It´s just a matter of duty but quite a bit of work (as usual in vector analysis), so I will not break it down any further, sorry.
