# What is the volume of the solid produced by revolving #f(x)=x^3, x in [0,3] #around #y=-1#?

##### 1 Answer

Feb 7, 2018

See explanation below

#### Explanation:

We have a revolution solid with a hole inside because the spin axis is y=-1.

Consider a volume element with a width of

So, the volume of this volume element is

The sbstitution in that formula give us:

Integrating between 0 and 3 wil give us the volume requested

solving this integral we have: