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