# Homework Help: Volume by rotating a curve

1. Dec 9, 2009

### mikhailpavel

1. The problem statement, all variables and given/known data
Hey i have a problem here with volume by cylindrical shells. i wanted to find the given volume of the solid obtained by rotating the region bounded by the curves x=1+(y-2)^2 and x=2 about the x axis.

2. Relevant equations
we tried to integrating 2 phi f(y) dy with upper limit 3 and lower limit 1.

3. The attempt at a solution
we got the answer 33.5 but i dont think it is the correct one.
immediate help will be appreciable.

2. Dec 9, 2009

### Staff: Mentor

You are using cylindrical shells, but your formula is incorrect. A typical shell in this problem has a volume of 2pi*y*(x2 - x1)*dy

x2 is the x-value on the line x = 2, and x1 is the x-value on the parabola. You have graphed the region being revolved, right?

3. Dec 10, 2009

### mikhailpavel

can u tell me if my upper and lower limits are right because still i am not getting the right answer..i think!

4. Dec 10, 2009

### HallsofIvy

Yes, the two curves intersect at (2, 1) and (2, 3) so y ranges between 1 and 3.