Rotating integrals and circles

[lemurs]

kay had a question which i got zero on and now trying to figure out how the hell to do the question.

Given x^2 + (y-1)^2 =1 rotated about the x-axis.

if i could get the solution so i can review it so i can have a better idea how to do it on the mid term.

Hint:, I was told to do with respect to the y-axis.

 

[StatusX]

So how do you set up the integral?

 

[lemurs]

well that part of the stuff that confused me.

I set it upas
x = sqrt(1- (y-1)^2)

so my intergral becomes

from 0-2 2(pi) y sqrt(2y - Y^2).

but given that. we end up with a nasty integration... I tryed to get help form soem one but we vouldn't figure it out..

 

[StatusX]

That's right. Try the substitution u=y-1. You'll end up with the sum of two integrals, one you can do by another substitution and the other you can do just knowing the area of a circle.