Question

Let a + b = 4, where a < 2 and let g(x) be a differentiable function. If dg/dx > 0 for all x, prove that ∫ g(x) (for x → 0,a) dx + ∫ g(x) (for x → 0,b) dx increases as (b - a) increases.

Answer 1

Hence, F(t) increases with t, therefore, F(t) increases as (b - a) increases.