Volume by Rotating a Curve: Finding the Solid Between Two Curves

[mikhailpavel]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

we got the answer 33.5 but i don't think it is the correct one.
immediate help will be appreciable.

 

[Mark44]

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?

 

[mikhailpavel]

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

 

[HallsofIvy]

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