, , ,

To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius and .

where

Remove parentheses.

By the Power Rule, the integral of with respect to is .

Combine and .

Substitute and simplify.

Evaluate at and at .

Simplify.

Raise to the power of .

Raise to the power of .

Combine the numerators over the common denominator.

Subtract from .

Combine and .

Move to the left of .

Find the Volume y=x , y=0 , x=2 , x=4