# Green's Theorem

• February 26th 2010, 08:11 AM
qwesl
Green's Theorem
How do you compute the area of the curve $r=10sin(18\theta)$ using Green's Theorem (ie. $\oint F_{1}dx+F_{2}dy =\int\int (\frac{\delta F_{2}}{\delta x}-\frac{\delta F_{1}}{\delta y})dA$)

I tried $F_{1}=-y/2$ and $F_{2}=x/2$

$x=\theta$
$y=10sin(18\theta)$
$dx=d\theta$
$dy=180cos(18x)d\theta$

But I get this integral which I can't solve

$\frac{1}{2}\int^{2\pi}_{0}(180\theta cos(18\theta)-10sin(18\theta))d\theta$