Gravitational Field Problem - Integrate?

[Mmm_Pasta]

Homework Statement

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.)

Homework Equations

F=GMm/d^2
g=GM/d^2

The Attempt at a Solution

Since the mass varies depending what L is, the equation would be Gdm/(x₀-L)^2 which is Gλdx/(x₀-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.

 

[cepheid]

The Attempt at a Solution

Since the mass varies depending what L is, the equation would be Gdm/(x₀-L)^2 which is Gλdx/(x₀-L)^2.

This looks close, although I think it should be (x₀ - x)² in the denominator, since you are talking about the contribution due to the infinitesimal mass element located at position x.

Do I then integrate to get rid of the dx? If I do I am not sure what dx would be to begin with.

What do you mean by "I don't know what the dx would be to begin with?" Do you know calculus?

 

[Mmm_Pasta]

I put L because x₀ is greater than L, but now I know why it is x. Never mind about the dx; I worded the question wrong, but I know now. Thanks. =)