# Thread: prove area of ellipse

1. ## prove area of ellipse

Show that the area of ellipse

x^2/a^2 + y^2/b^2 =1 is pi*ab.

2. It's symmetric with respect to the $y$ axis.

We consider to compute the half area of the ellipse, then when you get the final answer, multiply by 2 and you are done.

It remains to compute $\int_{-a}^a\sqrt{b^2\left(1-\frac{x^2}{a^2}\right)}\,dx$