Example 2 Video Exampled' Since f(x) = 5 + x2 is continuous on the interval [2, 4), the mean value theorem for integrals says there is a number c in [2, 4) such that (5 + x2)dx Nc) 4 (2) . In this particular case we can find c explicitly. using the formula b Th e refore 5 + so = f(x) dx, we find the average value of the function f g, so the value of c satisfies Nc) So in this case there happen to be two numbers c 2 in the interval [2, 4) that work in the mean value theorem for integrals. 15 10 2 4 6