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    Surface of Revolution

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    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.

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    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, ...

    Solution Summary

    The method of finding a surface of revolution is discussed.