This is an attempt at generalizing Newton\'s zero gravity field inside a hollow

Question

This is an attempt at generalizing Newton's zero gravity field inside a hollow spherical shell. Above is an ellipsoid make of concentric circles around the x-axis. The attempt is to find the total gravitiational force on the origin. My questions is how do I express the infinitesimal thickness of the ring located at x of radius r. I know the arclength of an ellipse is in the form of the elliptic Integral. Do I take the derivative of the elliptic Integral to get the infinitesimal thickness of the ring? Then if so is the integral below a correct beginning?

Explanation / Answer

Hi I have done the solution for this in my notebook. But the solution is too big , I cannot type it here because very less time is remaining.. So please rate me Lifesaver and I'll share the answer with you through email or cramster inbox. I don't do this generally, but I have no other option here because there's very less time left... you need not worry as I have the solution ready

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