Question

given an area bounded by the curve y=xe^-x the x axis and maximum ordinate find the moment of inertia with respect to x axis

Answer 1

the maximum occurs at (1,1/e), so the moment is (assuming a density of 1)

∫ r^2 dm = ∫[0,1] (xe^-x)^2 dx
which you can evaluate using integration by parts.
Post your work if you get stuck.