The region P is bounded by the x axis , the line x =1 and the curve y = 1/x. show that
a. the area of region P is infinite.
b. show that the solid of revolution obtained by rotating region P about the x axis is finite.
Am I correct?
Yes this is perfectly correct, the shape is know as Gabriel's Horn and the problem is sometimes reffered to as The Painter's Paradox.
Gabriel's Horn - Wikipedia, the free encyclopedia
It's quite weird that you can fill the horn to the brim with a finite amount of paint, but to paint the outside you need an infinite amount.