What is the volume of the solid produced by revolving #f(x)=1/x-1/x^2, x in [2,6] #around the x-axis?
The portion of the graph of f(x) in the interval [2,6] looks like in the figure below:
If this portion is revolved around x-axis, the volume of the solid so generated can be worked out as follows:
Consider an element of the area enclosed by the x-axis and the curve, at a distance x from the origin and length y= f(x). If this is rotated about x-axis a circular disc of area