Question

Anybody have any ideas on how to find the area of an ellipse by using an iterated integral? Please see attached.....

Answer 1

\[y=\pm b\sqrt{1-\frac{x^2}{a^2}}\]
\[\int_{-a}^{a}\int_{b\sqrt{1-\frac{x^2}{a^2}}}^{-b\sqrt{1-\frac{x^2}{a^2}}}~\frac{x^2}{a^2}+\frac{y^2}{b^2}-1~~dy~dx\]

maybe??

Answer 2

hmmmm I think you are on to something. My teacher said we will need to use trig substitution for one of the integrals and that definitely looks like a trig substitution integral!....gotta make dinner but i'll be back to see if i can solve this....thanks!

Answer 3

Here's what I got, but it's not finished yet.