You can find information here
http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx but if you're to lazy to read the whole article I'll give you the formulas you need
\(\displaystyle \displaystyle S\, =\, \int\, 2\pi y\, ds\)
. . . . .\(\displaystyle \mbox{rotation about }\, x\mbox{-axis}\)
\(\displaystyle \displaystyle S\, =\, \int\, 2\pi x\, ds\)
. . . . .\(\displaystyle \mbox{rotation about }\, y\mbox{-axis}\)
You need the upper one. For the surface element insert
\(\displaystyle ds\, =\, \sqrt{\strut 1\, +\, \left(\dfrac{dy}{dx}\right)^2\,}\, dx\, \mbox{ if }\, y\, =\, f(x),\, a\, \leq\, x\, \leq\, b\)
\(\displaystyle ds\, =\, \sqrt{\strut 1\, +\, \left(\dfrac{dx}{dy}\right)^2\,}\, dy\, \mbox{ if }\, x\, =\, h(y),\, c\, \leq\, u\, \leq\, d\)
Again it is the upper one you need since you have a function y=f(x) and want to rotate around the x-axis. Hope this helps. If you need help with the process let me know.
