Solid of revolution in cylindrical coordinates

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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...