# Thread: bounded solid

1. ## bounded solid

Let S be a solid bounded by the xy-plane, on the side by the cylinder $\displaystyle x^2+y^2=2x$ and above by $\displaystyle x^2+y^2+z^2=4$.

Set up a triple iterated integral in rectangular coordinates which represents the volume of the solid S.

I know that the first integral is dx from 0 to 2, but how to obtain other?

2. Originally Posted by jacek
Let S be a solid bounded by the xy-plane, on the side by the cylinder $\displaystyle x^2+y^2=2x$ and above by $\displaystyle x^2+y^2+z^2=4$.

Set up a triple iterated integral in rectangular coordinates which represents the volume of the solid S.

I know that the first integral is dx from 0 to 2, but how to obtain other?
The inside integral is a surface to surface ($\displaystyle z=0$ to the sphere) whereas the outer two integrals is a circle centered at $\displaystyle (1,0)$ and radius 1 -
$\displaystyle \int_0^2\int_{-\sqrt{2x-x^2} }^{\sqrt{2x-x^2}} \int_0^{\sqrt{4-x^2-y^2}}dzdydx$

although I think cylindrical polar coords would be the way to go. :-)