# What is the surface area produced by rotating #f(x)=x^3-8, x in [0,2]# around the x-axis?

##### 1 Answer

Jun 21, 2018

first find dS, note the radius of the rotation is x.

to solve make a substitution of

#### Explanation:

If you make the substitution with w your integral becomes

with a trigonometric substitution

the integral becomes

which you can solve by parts or using a table.