Some help needed in interpreting a problem -- Keplerian velocity 1. The problem statement, all variables and given/known data Code (Text): Consider a galaxy made by a uniform thin disk of surface density ρ. The total mass of the galaxy is M = 1040 kg and its radius r = 1020 m. Integrate numerically the gravitational force as a function of the distance from the center (for distances up to the galaxy’s radius) and plot the Keplerian velocity as a function of the distance from the center. I formulated an integral at which I attempted to calculate numerically, but the solutions were all over the place (as if the integral did not exist / did not converge.) In this problem, when it asks for the gravitational force, does it mean on any arbitrary mass within the disk/galaxy? And am I supposed to model this as a sum of forces given by small mass elements within the galaxy? (i.e. dF = Gm/r^2 dM, where G is the gravitational constant, m is the mass of an arbitrary body, dM is a mass element of the galaxy, and r is the distance between these) If this is correct, I came up with the following integral: F = ∫Gmρ(x-r0)/((x - r0)2 + y2)3/2da where I have chosen a Cartesian coordinate system in x and y, and so this integral is taken over (x,y) in a disk of radius r = 1020 m. r0 is the distance from the center of the galaxy. I realize now I should have chose a polar coordinate system due to the symmetry of the problem, but nonetheless, you can see with the integrand, it goes to infinity when (x, y) -> (r0, 0). Have I done something incorrectly or mis-interpretted the problem?