Surface Area of an Astroid
I have a presentation tomorrow on a homework problem and I am stuck on the following problem:
Find the surface area of the astroid x^(2/3) + y^(2/3) = 1
Since it is symmetric I leave the bottom part out and revolve the upper part around the y-axis and multiply the result by 2. Limits of integration is from 0 to 1.
So far I think I am on the right track, but when I try to integrate this it gets really ugly.
I transformed the above equation into x=f(y) notation (since it is rotated around y-axis) and got y= (1-x^(2/3))^(3/2)
When plugged into the calculator I get a somewhat reasonable answer of 2Pi for the surface area of the whole asteroid.
Does anyone have any suggestions on the integration (I tried several different things but always get stuck)?