Suppose that f is integrable on [a,b] and define the functions f*(x) = | F(x), f(x)20 [0, and f-(x)=- f(x) 2 0 f(x)<0 f(x)<0° Prove that f¯ are integrable on [a,b].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Course : Real Analysis

 

Suppose that f is integrable on [a,b], and define the functions
rw-
f(x) > 0
f*(x) = f(x), f(x)20
and f"(x)
f(x)
0,
f(x) <0
f(x)<0
Prove that
fr are integrable on [a,b].
Transcribed Image Text:Suppose that f is integrable on [a,b], and define the functions rw- f(x) > 0 f*(x) = f(x), f(x)20 and f"(x) f(x) 0, f(x) <0 f(x)<0 Prove that fr are integrable on [a,b].
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