I have a few problems I'm trying to solve and could use some help on

1) y=4-x^2, y=2-x (rotate about the x axis)

So my inner radius is 2-x, my outer radius is 4-x^2

I integrate from x=-1 to x=3 because that's where they intersect.

So I integrate:

pi(4-x^2)^2 - pi(2-x)^2 which comes out to

48pi - pi4^5/5 + 64pi/3

2) y= secx, y=tanx, x=0, x=1

Integrate from 0 to 1, rotate about x axis

Inner radius is tanx, outer is secx.

So I have to integrate

pi(secx)^2 - pi(tanx)^2 = pisec^2x - pitan^2x =

pi integral sec^2x-sec^2x-1 = -pi(x)

3)y=2x, y=0, x = 1 (thus x=y/2)

Rotate about the line x=1

outside radius = 1-y/2

integratee pi(1-y/2)^2 which comes out to 2/3pi

Then I have to do the same shape, but with a different radius (about the line x=2 and limits of integration... so I figure if that one is right then the next one will be too.)