How to solve this integration problem problem did but got wrong answer

[mikhailpavel]

Homework Statement

Find the volume generated by rotating the region bound by the given curves about the x axis

Homework Equations

x=1+(y-2)^2, x=2

The Attempt at a Solution

i solved the problem using cylinder shells method. the solution equation i got was
integration of 2phiy(1+y^2-2y+4)dy. the upper limit of the equation i got was 3 and the lower limit was 1.
the answer i got was 142.42 but it came out to be wrong.
can anyone help me.

 

[Dick]

The length of your shell should be 2-(1+(y-2)^2), right? When I expand that, I don't get (1+y^2-2y+4). Can you check that part?

 

[mikhailpavel]

thank you i got it now...what i did in my solution was that i didnt subtracted x=2 from the equation x= 1+ (y-2)^2.
thanks for the help.