PROPOSITION 7.17. Suppose that ƒ, g : [a, b] → R are integrable. Then: (1) For any k € R, k. f is also integrable on [a, b], and ·b ·b S k. f(x) dx = k [ f(x) dx. a a (2) The function f + g is also integrable on [a, b], and [*(ƒ + 9) (x) dx = [*ƒ(x) dx + [*9(x)dx.
PROPOSITION 7.17. Suppose that ƒ, g : [a, b] → R are integrable. Then: (1) For any k € R, k. f is also integrable on [a, b], and ·b ·b S k. f(x) dx = k [ f(x) dx. a a (2) The function f + g is also integrable on [a, b], and [*(ƒ + 9) (x) dx = [*ƒ(x) dx + [*9(x)dx.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Can you please simply prove both propositions (1 & 2) from the attached note?
For proposition (1):
Please prove it in the case that k < 0 or k = 0.
Thank you!
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