For this question:
Calculate $\int \!\!\! \int E\cdot \vec n d\sigma$ where S is the parametric surface $X(s,t)=[st,s^2,t^2]^T$, $0\le s\le t\le 1$, and the E is the vector field $E(x,y,z)=[3yz,zx,2xy]^T$
Do I just use the formula:
$\int\!\!\!\int E(x(s,t))\cdot (\frac{\partial x}{\partial t}\times \frac{\partial x}{\partial s})dsdt$
Leading me to: $\int_0^1\int_0^1 (3s^2t^2,st^3,2s^3t)\cdot (0,0,-s)=\int_0^1\int_0^1 -2s^4t=-\frac{1}{5}$
Is that correct?