Can someone please help;
I keep getting a really ugly answer I'm sure is wrong
Use Green's Theorem area formula to find the ares of the region: the ellipse
r(t)= (acost)i + (bsint)j t between 0 and 2pi
The area formula has a few different (equivelent) ways to be written so here is one
$\displaystyle A=\oint_{C}xdy=-\oint_Cydx $
We can use either one so with the first one we get
$\displaystyle A=\int_{0}^{2\pi}a\cos(t)(b\cos(t)dt=ab\int_{0}^{2 \pi}\cos^{2}(t)dt=\frac{ab}{2}\int_{0}^{2\pi}(1-\cos(2t))dt=$
$\displaystyle \frac{ab}{2} \cdot [t-\frac{1}{2}\sin(2t)]\bigg|^{2\pi}_{0}=\pi ab$