I have to find the surface area formed by rotating $y=\ln(x)$, $1\le x\le e$, about the $y$-axis. I have done the following steps but I am not sure about it. Is there any hint/insight for me on it? Thank you. Here is the link to it:
2026-04-08 22:45:12.1775688312
Surface area of $y = \ln(x)$ rotated about y-axis
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Try the change of variables $e^y=z$ and after that another change of variables $z=\sinh(u)$