Help with Calculus!!! Surface area of revolution stuff

Question

anonymous · Answer

Compute the surface area of revolution of $$f(x) = 2/3(1+x^2)^\frac{ 3 }{ 2 }$$

anonymous · Answer

$$\frac{ 2 }{ 3 }(1+x^2)^\frac{ 3 }{ 2 }$$ just to avoid confusion

zepdrix · Answer

Mmmmmmmmmm ok ok ok I think I remember how to do these >.<
Where you stuck at?

zepdrix · Answer

So lemme try to remember....
We split up our curve into "little small" infinitesimal pieces that we call of length $\Large\rm ds$.

To find the arc-length of the figure we add up all of these little pieces,$$\Large\rm L=\int\limits ds$$To find surface area, we instead spin this ds around one of the axes.
So we'll multiply by the circumference.$$\Large\rm S=\int\limits (2\pi x)ds$$or$$\Large\rm S=\int\limits (2\pi y)ds$$The radius depends on which axis we're spinning around +_+ You didn't specify that. Which one is it? :3

zepdrix · Answer

I'll assume we're spinning around the y-axis, that would make the most sense for this problem.

So our radius is x, yah?

zepdrix · Answer

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