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**1. The problem statement, all variables and given/known data**

A nonuniform thin rod of length L lies on the x axis. One end of the rod is at the origin, and the other end is at x = L. The rod's mass per unit length λ varies as λ = Cx, where C is a constant. (Thus, an element of the rod has mass dm = λdx.)

Determine the gravitational field due to the rod on the x axis at x = x0, where x0 > L. (Use the following as necessary: G, M, L, x0.)

**2. Relevant equations**

F=GMm/d^2

g=GM/d^2

**3. The attempt at a solution**

Since the mass varies depending what L is, the equation would be Gdm/(x

_{0}-L)^2 which is Gλdx/(x

_{0}-L)^2. Do I then integrate to get rid of the dx? If I do I am not sure what dx would be to begin with.