Let F(x) be defined for x > 0 by F(x) := (n - 1)x - (n -

Question:

Let F(x) be defined for x > 0 by F(x) := (n - 1)x - (n - 1)n/2 for x ∈ [n - 1, n], n ∈ N. Show that F is continuous and evaluate Fʹ(x) at points where this derivative exists. Use this result to evaluate ∫ba [[x]]dx for 0 < a < b, where [x]] denotes the greatest integer in x, as defined in Exercise 5.1.4