# What is the surface area of the solid created by revolving #f(x) =2x^3-2 , x in [2,4]# around the x axis?

##### 1 Answer

Feb 26, 2017

#### Explanation:

The surface area of a solid created by rotating a function

#S=2piint_a^bf(x)sqrt(1+(f'(x))^2)dx#

Here,

#S=2piint_2^4(2x^3-2)sqrt(1+(6x^2)^2)dx#

#S=2piint_2^4(2x^3-2)sqrt(1+36x^4)dx#

This cannot be easily integrated, so plug this into a calculator.

#S=49266.1936...#