MATH 350, Homework 11, problems 1-3.
-
If f : [a,b]→ R is decreasing prove that f is
integrable. [Cf. Problem 9, 5.1.]
- 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.]
- 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.]