Integration(volume) using cylindrical shell method..?

Question

The area bounded by y=x^2 and x=y^2 is to be revolved about the

x-axis:

FInd the volume if the solid generated?

Here is what I have done, so far,,

http://img354.imageshack.us/my.php?image=cylinderet8.jpg

thnks!

Answer 1

volume generated by y =x^2  is integration from 0 to 1 of pi*y^2 dx = 0 to 1 of pi*x^4 dx = pi/5

similarly for y = x^(1/2)

volume generated by y =x^(1/2)  is integration from 0 to 1 of pi*y^2 dx = 0 to 1 of pi*x dx = pi/2

subtract these two for getting the volume generated by area bounded = pi/2 - pi/5 = 3*pi/10