Note: * = infinite
Suppose that the function f:[0,*) -> R is continuous and strictly increasing, and that f:(0,*) -> R is differentiable. Moreover, assume f(0) = 0. Consider the formula:
the integral from 0 to x of f + the integral from 0 to f(x) of f^-1 =xf(x) for all x>= 0.
How can I provide a geometric interpretation of this formula in terms of areas and then prove this formula.
Do I use the Identity Criterion?
A functional relation is proven. The solution is comprehensive.