Even number problem in book ...volume

dimanche 1 septembre 2013

1. The problem statement, all variables and given/known data

Hey, I got an even number from my book trying to double check it so if you wouldn't mind I would appreciate some comfirmaion or denial.

Find the volume of the solid obtained by rotated te region bounded by the given curves about the specificed line.

y = x, y =0, x =2, x =4 : about x = 1

2. Relevant equations

I set up this integral

I = ∏∫ dy - ∏(1-y^2)^2 dy

I did this integral between [0,1]

3. The attempt at a solution

I got ∏( y-(y^5/5) + (2/3)y^3 - 1)

I worked it out and got (7/15)∏

Yes no maybe so ?Thx