
Green's Theorem
How do you compute the area of the curve $\displaystyle r=10sin(18\theta)$ using Green's Theorem (ie.$\displaystyle \oint F_{1}dx+F_{2}dy =\int\int (\frac{\delta F_{2}}{\delta x}\frac{\delta F_{1}}{\delta y})dA $)
I tried $\displaystyle F_{1}=y/2$ and $\displaystyle F_{2}=x/2$
$\displaystyle x=\theta$
$\displaystyle y=10sin(18\theta)$
$\displaystyle dx=d\theta$
$\displaystyle dy=180cos(18x)d\theta$
But I get this integral which I can't solve
$\displaystyle \frac{1}{2}\int^{2\pi}_{0}(180\theta cos(18\theta)10sin(18\theta))d\theta$