a) Find the average value of f(x) = x^n, where n is a positive integer, on the interval [a, b].

b) Use Mean Value Theorem for Integrals and show that: e^x x + 1, for all x R

c) Find the function f(x) so that, for x 0, its arc length in the interval [0, x] is equal to 2x+f(x)