You are correct about part a.
part b would be, using shells:
I need help with the following problem:
Suppose the region R is bounded by the curves y=2x + 1, y=2cos(2x),x=1, and x=3.
In each part below, I need to set up the integral required to find the volume of the solid obtained by revolving the region R above about the indicated line. I can use either washers or shells, whichever is appropriate.
a.) about the line y=-2
b.) about the line x=-2
For part a, I think you would set it up as ∫[from 1 to 3] Pi ((2x+1)+2)^2 - ((cos(2x))+2)^2 dx using washers.
I am not really sure how you would go about setting up part b, but here is what I guessed you would do: ∫[from 1 to 7] Pi(3+2)^2 -(1+1)^2 dy using washers.
Have I set either of these integrals up correctly? and if not I would appreciate any help explaining how you would go about setting them up correctly. Thanks in advance to anyone who can help me.