I did the following question two ways; with vertical strips and with horizontal strips. I got two slightly different answers [ rho*(13/4 + 6ln(2)) with vertical strips and rho*(13/4 - 6ln(2)) with horizontal strips]. I can't figure out which (if either) is the correct answer or where I went wrong.

Here is the question:

Consider the thin plate of constant density rho [mass/unit area] bounded by the curves:

y=ln(x), y=0, and x=2

Find the first moment (moment of mass) of this plate about the line x=4.