Suppose that ( is increasing on [(, b] and

Prove that

And give a physical interpretation of this result. Let F(x, y) = [y - x][((y) - ((x)] and use the hint of Problem 41.
Consider the double integral of
F(x, y) = [((x)g(y) - ((y)g(x)]2
Over the rectangle R = {(x, y): ( ( x ( b, ( ( y ( b}.

f(x) dx 0. af(x) dx a +b f(x) dx 0