I need to find a formula for the surface area of a solid of revolution rotated around the $y$-axis. The curve is $f(x)=x^2$ on $[0,1]$. However, my answer must be in terms of $f$, not $f^{-1}$.
Surface area of revolution about $y$-axis in terms of $f(x)$
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calculus
integration
solid-geometry