Find the average value fave of the function f on the given interval. f (x) = x2 / (x3 + 14) 2, [-2, 2] fave =

Let x indicate the dimensionless quantity x = k/k F. In the interval 0 ≤ x ≤ 1 the function F (x) varies from 1 to 1/2; it is easily seen that its average value is just 3/4; in fact Fav = ∫ 1 0 x2F (x) dx / ∫ 1 0 x2dx=3 ∫ 1 0 x2F (x) dx=34. (C. 5) The indefinite integral ∫ x (1-x2) ln1+x1-xdx = 1 2 x - 1 6 x3 - 14 (1-x2) 2ln1+x1-x has been ...