How to Find the Area of the Interior Using a Parametrization of a Curve?

[mmmboh]

Find a parametrization of the curve x^2/3+y^2/3=1 and use it to
compute the area of the interior.

What I did was y=(1-x^2/3)^3/2

I then integrated this function from 0 to 1 (using maple since it is a crazy integral) and got the answer to be 3/32 $$\pi$$.

However this is wrong, I probably wasn't suppose to do it the way I did anyway considering that the integral is so complicated.

So what should I do? I am learning Green's theroem right now if that helps, although I may have skipped ahead in it a bit I'm not sure.

Thanks.

Edit: Hm ok I have figured out what to do, the answer is 3/8 pi. How come my original answer is 1/4 of this though?

 

[tiny-tim]

Hi mmmboh!

Find a parametrization of the curve x^2/3+y^2/3=1 …

They want you to use a parametrisation.

For example, if it were x²+y²=1, you'd use x = cosθ, y = sinθ.