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$f:[a,b]\rightarrow\mathbb{R}$ is continuous and $R_f\subset\mathbb{R}^3$ is the solid of revolution that resulted from the rotation of the graph of $f$ around the x-axis.

Evaluate $\mu(R_f)$ [$=$ Volume of the body (as far as I know)].

Use cylindric coordinates, g, with

$g:]0,\infty[\times]0,2\pi[\times \mathbb{R} \rightarrow \mathbb{R}^3$\ $ (\mathbb{R}_0^+ \times \{0\} \times \mathbb{R}) $

$(r,\phi,z)\rightarrow(r \cos \phi, r \sin \phi, z)$

This is a bonus problem on my problem set this week. As it is a bonus problem we did not do this during the lecture.

Can someone help me with it since I have no idea how to start...

kaos
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  • Are you expected to give a formula in terms of $f$? There isn't really a global answer for the problem that's better than that... – Steven Stadnicki Jun 18 '15 at 23:53
  • Thats my problem.. I dont know what is expected of me here. But I think I should find a general formula for the volume of the body using cylindrical coordinates. – kaos Jun 18 '15 at 23:56

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