A surface of revolution is a surface that is generated by
revolving a plane curve about an axis that lies in the same plane as
the curve. For example, the surface of a sphere can be generated by
revolving a semicircle about its diameter.
Surface Area. Suppose that f is a smooth, nonnegative
function on [a,b] and that a surface of revolution is generated by
revolving the portion of the curve y=f(x) between x=a and x=b about the
x-axis. Then the following definite integral defines the area of the
surface of revolution
Example
Find the area of the surface that is generated by revolving the
portion of the curve y=x3 between x=0 and x=1 about the x-axis
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