What happens to a riemann integral value if I change a finite number of points of the integrand ? I've read it stays the same but don't know the proof.
Asked
Active
Viewed 29 times
0
-
Sketch of the proof: If you change a function $f$ at finitely many points you get another function $f_2$. The function $f-f_2$ is zero almost everywhere, in the sense that it is not zero only at finitely many points. Now $$\int f = \int f_2 + \int (f-f_2)$$ and the latter integral is zero because a function which is zero almost everywhere has zero integral. – Crostul Oct 20 '22 at 11:10
-
Thank you. Since the latter integral is piecewise continuous you break it and then it's parts go to zero.Am I right? – SotirisD Oct 20 '22 at 12:31
-
You are right. That concludes the proof – Crostul Oct 20 '22 at 13:29