# Thread: volume of solid of the revolution

1. ## volume of solid of the revolution

Can someone show me how to get the points of intersection for this problem [i know one of them is (1,1)]
Problem:
Determine the volume of the solid of the revolution obtained by rotating about the Y-axis the region bounded by y = 5th sqrt of (x) AND y = 2x^2-3x+2 that lies in the first quadrant??

Any help greatly appreciated

2. By 5th sqrt of (x) do you mean $\displaystyle \sqrt[5]{x}$?

I set both functions equal to each other. I tried to solve it, but it becomes a 10th degree polynomial, which I then ran through Mathematica and it has no closed form solution i.e. you will have to find the second point of intersection numerically.

3. Actually, that's not the problem! The problem is that the two graphs do NOT intersect! There is NO bounded region to rotate around the y-axis.

4. Actually there is a region as show in the graph