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Problem 38 Easy Difficulty

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 $.

Answer

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

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Video Transcript

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