Let a, b = R. Let f : [a, b] → R be an integrable function. Let g: [a, b] → R be a function which agrees with f at all points in [a, b] except for one, i.e. assume there exists a c = [a, b] such that g(x) = f(x) for all x = [a, b]\{c}. And g(c) < f(c). Prove that g is integrable on [a, b] and that fog(x)dx = So f(x)dx. Hint: Prove that g(x) - f(x) is integrable and the integral is 0.

Let a, b = R. Let f : [a, b] → R be an integrable function. Let g: [a, b] → R be a function which agrees with f at all points in [a, b] except for one, i.e. assume there exists a c = [a, b] such that g(x) = f(x) for all x = [a, b]\{c}. And g(c) < f(c). Prove that g is integrable on [a, b] and that fog(x)dx = So f(x)dx. Hint: Prove that g(x) - f(x) is integrable and the integral is 0.

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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