The Mean Value Theorem for Integrals states that there must be a point € x in the interval [€ a, € b] where the exact function value actually equals the average function value. That is, there is a solution to the equation f(x)= 1 b −a f(x) dx a b ∫. We can find the point € x several ways: (i) Find the average value € c “by hand” and then solve f(x) = €