Question

How do you find the volume of the solid obtained by rotating the region bounded by the curves `f(x)=3x^2` and `g(x)=2x+1` about the x axis?

Answer 1

I found: `200pi/81`

Explanation:

First let us see the area that will be rotated:

the two graphs meet at `x=1` and `x=-2/3` (values obtained solving the system formed by the two equations:
`{y=3x^2`
`{y=2x+1`
We can use the "Cylinder" method to evaluate the volumes of the solid generated by the first function (line) and then subtract the volume of the second (parabola) as: