So I had a question involving Surface Area.

Find the surface area generated by revolving the curve $x = y^3$ about the $y$-axis for $0 \leq y \leq \sqrt[4]{11}$.

(a) $23\pi\quad$ (b) $37\pi\quad$ (c) $46\pi\quad$ (d) $62\pi\quad$ (e) $73\pi\quad$ (f) None of these

This was my Attempt but I got stuck with trying to integrate the stuff under the radical.

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Hint: $\int y^3(9(y^4+\frac19))^{\frac12}\operatorname dy=\frac32(y^4+\frac19)^{\frac 32}+C$.


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