2. If f is continuous on [0, 1] such that x* f(x) dx=0, for n=0, 1, 2, 3,.. then show that f(x)3D0 on [0, 1].
2. If f is continuous on [0, 1] such that x* f(x) dx=0, for n=0, 1, 2, 3,.. then show that f(x)3D0 on [0, 1].
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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Proof by Weierstrass app. Theorem
![2. If f is continuous on [0, 1] such that
x* f(x) dx=0, for n=0, 1, 2, 3,...
then show that f(x)=0 on [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18fff3b8-0155-477b-ba22-fa831ded4dd5%2F90566a69-55ec-45c3-a848-9a36e7ac4fa8%2F8zrb7u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. If f is continuous on [0, 1] such that
x* f(x) dx=0, for n=0, 1, 2, 3,...
then show that f(x)=0 on [0, 1].
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