MATH 350, Homework 11, problems 1-3.

  1. If f : [a,b]→ R is decreasing prove that f is integrable. [Cf. Problem 9, 5.1.]
  2. Let f and g be integrable function on the interval [a,b], and define F(x)=max{f(x),g(x)}. Show that F is integrable on [a,b]. [Cf. Problems 12(a), 13(a), 5.1.]
  3. If f is continuous on [a,b] and satisfies cdf(x) dx =0 for every a<c<d<b then f≡0. [Cf. Problem 19, 5.1.]