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# Let $L$ be the length of the curve $y = f(x)$ , $a \le x \le b$, where $f$ is positive and has a continuous derivative. Let $S_f$ be the surface area generated by rotating the curve about the x-axis. If $c$ is a positive constant, define $g(x) = f(x) + c$ and let $S_g$ be the corresponding surface area generated by the curve $y = g(x)$, $a \le x \le b$. Express $S_g$ in terms of $S_f$ and $L$.

## $$S_{g}=S_{f}+2 \pi c L$$

#### Topics

Applications of Integration

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### Video Transcript

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