Answered: Let f, g : [a, b] → R be two Riemann…

Let f, g : [a, b] → R be two Riemann integrable functions such that the set {x ∈ [a, b] : f(x) = g(x)} is dense in [a, b]. Show that the integral f(x) dx = g(x) dx.

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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Question

Let f, g : [a, b] → R be two Riemann integrable functions such that

the set {x ∈ [a, b] : f(x) = g(x)} is dense in [a, b]. Show that the integral

f(x) dx = g(x) dx.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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