I'm trying to find the volume of the interior solid of the cylinders $y^2=2x$, $x^2+y^2=4x$, under the plane $x+z=5$ and above $z=0$.
Which the integral is:
$$\int_{0}^{2}\int_{\sqrt{2x}}^{\sqrt{4x-x^2}}\int_{0}^{5-x} dzdydx= 6\pi-\frac{224}{15}$$
But it's difficult to calculate, so i want to change it to cylindrical coordinates, but i can't find the right $r$ to make the integral.
$$\int_{0}^{\pi}\int_?^?\int_0^{5-r\cos(\theta)}rdzdrd\theta$$