Applications of Integration

Question

The region between the graphs of x=y² and x=2y is rotated around the line y=2.

The volume of the resulting solid is:

Answer 1

Notice that the intersection points are (0,0) and (4,2). Then using shell method we have

\int_0^2 2pi(2-y)(2y-y)dy=8pi/3

(\int_0^2 means integral with limit points 0 and 2)