# Thread: Green's Therorem question 2 ...

1. ## Green's Therorem question 2 ...

Let C be the positively oriented circle . Use Green's Theorem to evaluate the line integral .

2. Originally Posted by iwonder
Let C be the positively oriented circle . Use Green's Theorem to evaluate the line integral .
Here, $f\left(x,y\right)=4y$ and $g\left(x,y\right)=11x$

Thus, $\frac{\partial f}{\partial y}=4$ and $\frac{\partial g}{\partial x}=11$

Thus, by Green's Theorem,

$\oint_C 4y\,dx+11x\,dy=7\iint\limits_R\,dA$

Note that the Region R is just a circle of radius 1!!! Thus, $\oint_C 4y\,dx+11x\,dy=7\iint\limits_R\,dA=\dots$

Does this make sense?

3. IT DOES!!
thankyou very much!!