Rotation around a curve. Find the Volume.

[Cbarker1]

I am thinking about how to find the volume rotate around its function.


Let f be a function of x in the interval [a,b] . The function could be any curve. And the curve is rotation around itself. Would there exist a volume of the curve? And how to find the volume


Thank you

CBARKER1

 

[Fantini]

Well, here are some thoughts. We need some regularity on the function, such as continuity, otherwise this can be very messy and the question won't make sense. Second, what do you mean by "rotated around itself"? If you consider a simple case, i.e. a constant function, there's no volume. You're just rotating a line.