# Real Analysis: Geometric Interpretation in Terms of Areas

Not what you're looking for? Search our solutions OR ask your own Custom question.

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?

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:37 am ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-geometric-interpretation-in-terms-of-areas-10029

#### Solution Summary

A functional relation is proven. The solution is comprehensive.

$2.49