1. ## Green's Therorem...

Let C be the positively oriented square with vertices , , , . Use Green's Theorem to evaluate the line integral .

2. Originally Posted by iwonder
Let C be the positively oriented square with vertices , , , . Use Green's Theorem to evaluate the line integral .

Note that $f\left(x,y\right)=7y^2x$ and $f\left(x,y\right)=6x^2y$

Thus, $\frac{\partial f}{\partial y}=14xy$ and $\frac{\partial g}{\partial x}=12xy$

Also note that the region R is bounded by the lines $x=0,~x=2,~y=0,~y=2$

Thus, by Green's Theorem,

$\oint_C7y^2x\,dx+6x^2y\,dy=-2\int_0^2\int_0^2xy\,dx\,dy$

Can you take it from here?