Question

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis.
y=4/x, y=0, x=2, x=3

I know you have to integrate from 2 to 3 but im not sure what the integral should be

Answer 1

Consider a small elemental cylinder of radius x (between 2 and 3), and height=y=4/x, and thickness dx.
The volume of the elemental cylinder is therefore, by the usual formulae:
circumference*height*thickness
=2πx * y * dx
=2πx * 4/x * dx
=8πdx
Integrate the elemental volume for x=2 to x=3 to get the total volume.