# Thread: Help setting up integral using shells or washers

1. ## Help setting up integral using shells or washers

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.

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.

2. You are correct about part a.

part b would be, using shells:

$2{\pi}\int_{1}^{3}(x+2)((2x+1)-2cos(2x))dx$