Surface area of solid of revolution

If we revolve a curve y=f(x)  on the interval [a,b] about x axis, then we calculate area of resulting surface by breaking the curve into pieces as we did for arc length. A piece of curve of length dS at an average  distance y from x axis traces out a surface that is well approximated by a slice of a cone whose area is approximated by 2πydS.

\dpi{120} \mathbf{S=\int_{a}^{b}2\pi (radius)(arc length)dx}

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