If the ellipse has a uniform value the integral becomes the product between that value and the length of each beam through the ellipse. It should be possible to get an analytic expression for this length in terms of the ellipse parameters and the line parameters, although it might take some work to get this.
Alternatively if you have sufficient memory you can use the radon.m with an extremely high resolution phantom to get a good approximation.
It is linear, so the sum of the transforms of the individual ellipses should equal the transform of the sum of the ellipses (ie. the transform of your Shepp-Logan phantom).
