Find the volume of the solid

Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x² and y=4 about the line y=4. 

 

what is the volume?

Answer 1

The disk method looks to be easier than the washer method for this problem.

 

The integral over x is from -2 to 2  over a stack of thin disks each  with  volume  π (4 - x²)² dx 

 This integral can be carried out by expanding the squared binomial and then integrating term by term.

 

I got  ( 512/15) π