Double integration of 2 cylinders

I have to sketch the domain of the integration and evaluate the given iterated integrals.

I have 2 cylinders

1. $\displaystyle x^2+y^2 = a^2$

2. $\displaystyle y^2+z^2 = a^2$

The biggest problem for me is to write the integration, with the boundaries?

How do i find them?

Re: Double integration of 2 cylinders

Have you started with a sketch?

Re: Double integration of 2 cylinders

Well thats another problem.. I don't know how it should look like, i don't know how to plot it in Mathmatica..

Re: Double integration of 2 cylinders

The first is made of circular cross-sections in the x-y plane of radius a units, extending along the z axis.

The second is made of circular cross-sections in the y-z plane of radius a units, extending out in the x axis.

Re: Double integration of 2 cylinders

But how would it look like? Radius etc.