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Surface Area Formula: (Circumference X Arch Length)

For revolution about $x$-axis: $$S = \int_a^b 2\pi f(x)\sqrt{1+[f'(x)]^2}dx$$ For revolution about $y$-axis: $$S = \int_c^d 2\pi h(y)\sqrt{1+[h'(y)]^2}dy$$

In the surface area formulas above, I understand that the $f(x)$ will just be what $f(x)$ (aka $y$) equal (e.g. for $y=x+4$, $f(x)$ in that formula will be $x+4$) but I do not understand what $h(y)$ will be. Will it just be $f(x)$ in terms of $y$? (e.g. for $y = x+4$, $h(y) = y-4$)

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    Yes, you are correct.2011-07-07
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    Rotate your coordinate system by 90 degrees, then your height becomes the distance from the function to the y-axis.2011-07-07
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    @Matt: You are right. I think of it as reflection in the line $y=x$, thus interchanging the roles of $x$ and $y$. So just express $x$ in terms of $y$, like you did.2011-07-07

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