# Find the volume of the solid

1. May 22, 2009

### Emethyst

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

2. Relevant equations
Disk/washer method, shell method

3. The attempt at a solution
This question seemed easy enough, as I found the points of intersection for the 2 functions (these points being -1 and 3), then plugged each of these functions into the disk/washer method equation and tried to solve over [3,-1]. This did not get me very far, for I ended up with an answer higher than the 4pi I should have gained. This is the way I set up the equation:
V=pi$$\int(x+1-(4x^2/9))dx$$ (I already applied the squares to the functions inside the integral). I am wondering if I made a mistake setting this question up, or if I made a mistake with the closed interval I used. If anyone can point me in the right direction for this question it would be greatly appreciated, thanks in advance.

2. May 22, 2009

### squidsoft

Hi. You need to plot it carefully and look at it: the lower boundary of the region is the function y=2/3x in one part of the region, but is the x-axis in the second part of the region. So . . . break it up into two integrals.