Y=2*sqrt[x] y=0, x=3
We are using the following formula 2pi intergal of r(x) times the sqrt of 1 + (f'(x))^2.© BrainMass Inc. brainmass.com March 4, 2021, 5:47 pm ad1c9bdddf
Well, there is vagueness here. I am not sure whether the rotation has been about the x-axis or y-axis. Your question is about the method of integration. Well, I consider both cases i.e. rotation about x-axis and rotation about y-axis. y=0 implies that x=0, so the integral will be taken from x=0 to x=3.
Case I- About x-axis:
but we can merge the integrand expressions, ...
The method of finding a surface of revolution is discussed.