# What is the surface area of the solid created by revolving #f(x) = 6x^2-3x+22 , x in [2,3]# around the x axis?

##### 1 Answer

Jun 21, 2016

#### Explanation:

around the x axis, the volume of revolution is

that looks horrendous and might be made simpler by a shift in axis. completing the square should ultimately make the algebra a little bit easier to bear

so

so

and the integral becomes