The area under the curve y= x^(-2/3) from x=1 to infinity is undefined. Yet if the region is rotated about the x-axis the volume of revolution IS defined as 3pie.
I've done the math but can't explain how it is so conceptually. The best I can come up with is that the area is not necessarily infinite just indeterminable. But I think that this may be b.s.
Any help would be greatly appreciated.