Question

by using the cylinder shell the volume of the solid when the region enclosed by y=x^2, x=2, x=3, and y=0 is revolved about the y-axis.

Answer 1

a drawing tends to be quite helpful for these

Answer 2

recall that a shell is just the lateral area of a cylndar, so circumference times height

Answer 3

\[\int 2\pi rh\]

Answer 4

integrate: 2pi rh

since r = x, and h=x^2 this simplifies to just

integrate: 2pi x x^2 from x=2 to 3