Question

Using disks or washers, find the volume of the solid obtained by rotating the region by the curves y=x^(2) and y=4 about the line y=4

Answer 1

Using the disk method, do you see how the radius of each disk will be
\[\text{radius}=4-x^2?\]
The integral will then be
\[\pi\int_{-2}^2(4-x^2)^2dx\]
Taking advantage of symmetry, you have
\[2\pi\int_{0}^2(4-x^2)^2dx\]