Following from a previous post:
Let $h_i, h_j, f_i,f_j$ continuous functions such that $f$ are increasing and $f(0)=0$, Assume that: $\forall x$ $$h_i (x)>h_j (x)$$ $$f_i (x)>f_j (x)$$ and
$$\int_{0}^\infty h_i (x) f_i (x)dx>0$$ $$\int_{0}^\infty h_j (x) f_j (x)dx>0$$ Then, prove that $$\int_{0}^\infty h_i (x) f_i (x)dx>\int_{0}^\infty h_j (x) f_j (x) dx$$
I tried several things but haven't work to prove if the statement is right or wrong...