# 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?

##### 1 Answer
Jul 4, 2015

I found: $200 \frac{\pi}{81}$

#### Explanation:

First let us see the area that will be rotated:

the two graphs meet at $x = 1$ and $x = - \frac{2}{3}$ (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: