proof of continuous functions are Riemann integrable
So let be fixed.
Let now be any partition of in i.e. a partition such that . In any small interval the function (being continuous) has a maximum and minimum . Since is uniformly continuous and we have . So the difference between upper and lower Riemann sums is
This being true for every partition in we conclude that .
|Title||proof of continuous functions are Riemann integrable|
|Date of creation||2013-03-22 13:45:34|
|Last modified on||2013-03-22 13:45:34|
|Last modified by||paolini (1187)|