(b) Let f [a, b] → R be a function which is continuous on [a, b] and differentiable on : (a, b). Show that the function F(x) = f f(t) dt is increasing on [a, b] if and only if f(t) ≥ 0 on [a, b].
(b) Let f [a, b] → R be a function which is continuous on [a, b] and differentiable on : (a, b). Show that the function F(x) = f f(t) dt is increasing on [a, b] if and only if f(t) ≥ 0 on [a, b].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(b) Let f: [a, b] →→ R be a function which is continuous on [a, b] and differentiable on
(a, b). Show that the function F(x) = f f(t) dt is increasing on [a, b] if and only
if f(t) ≥ 0 on [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81e03d6c-c953-47c6-a5f9-daf0571ac32a%2F466d72a4-6151-4777-90d9-54f46019f3a0%2Fl81yhss_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Let f: [a, b] →→ R be a function which is continuous on [a, b] and differentiable on
(a, b). Show that the function F(x) = f f(t) dt is increasing on [a, b] if and only
if f(t) ≥ 0 on [a, b].
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