# Find the volume of the region

1. May 21, 2009

### Emethyst

1. The problem statement, all variables and given/known data
Find the volume of the solid generated by the revolution of the region enclosed by y=x^2+2, y=2x+1 and the y-axis about the line y=3

2. Relevant equations
Disk/Washer method, shell method

3. The attempt at a solution
This one is stumping me no matter how I go about it. What I have done so far is use the disk/washer method by inputting x+3 in for f(x) and x^2-2x+1 (obtained from subtracting the two functions given) in for g(x):
V=pi$$\int$$((x+3)^2-(x^2-2x+1)^2)dx over [0,1]. I think that because of the location of the region on a graph, however, the x+3 might become x+2, and that I might have made a mistake in the way I set the formula up, but I do not know if/where I made this mistake. If anyone can point me in the right direction and point out any mistakes I made in setting up this question it would be greatly appreciated, thanks in advance.

2. May 21, 2009

### Staff: Mentor

What you want for your typical volume element is this:
$$\Delta V = \pi [(2x + 1 - 3)^2 - (x^2 + 2 - 3)^2]\Delta x$$
Simplify that a bit, and integrate between 0 and 1, and you should be good.