# Simplifying Integral

1. Jan 30, 2008

### apoptosis

Hello
Here is an integral question I have. It's a surface area problem, but i just have issues simplifying the square root before solving. Any help appreciated!

y=(1-x$$^{2/3}$$)$$^{3/2}$$, 0$$\leq$$x$$\leq$$1

My work:
dy/dx=-x$$^{-1/3}$$(1-x$$^{2/3}$$)$$^{1/2}$$
(dy/dx)$$^{2}$$=-x$$^{-2/3}$$(1-x$$^{2/3}$$)
=-x$$^{-2/3}$$+1

S=(insert integral with limits here) 2$$\pi$$xds
=2$$\pi$$x $$\sqrt{-x^{-2/3} +1+1}$$
=2$$\pi$$x $$\sqrt{-x^{-2/3} +2}$$

I'm not sure where to go after this...
thx

Last edited: Jan 30, 2008