... differentiable on [a, b] and f ' is integrable on [a, b], then Proof: Let P = {x0, x1, …, xn} be any partition of [a, b] By applying the mean value = f (b) − f (a ) theorem to each subinterval [xi ... improper integral diverges to dx we write ∫ 10∞1x and ∫01 1x dx = ∞ We can also define an improper integral over an unbounded interval Definition 7.3.10 c f be defined on [a, and integrable on [a, ... +finite f then the improper integral ∫ cb number, is said to converge to L ∫ ab f If L = ∞ (or – ∞), then the integral is said to diverge to ∞ (or – ∞) Example 7.3.9(a) Let f (x) = x – 1/3 for x...