http://i291.photobucket.com/albums/l...29/Capture.jpg

Printable View

- Oct 31st 2009, 08:27 PMxyzFinding if a function is Riemann Integrable
- Nov 1st 2009, 12:10 AMtonio

Well, going with the hint you could argue that since f(x) is continuous in , for any , then f is uniformly continuous there, so , and then: taking a partition P with n points of s.t. , we get .

Of course, we still need to deal with , but this is not problem: the difference can be made as little as wanted.

Now, not going with the hint is much simpler and shorter, but perhaps you guys haven't yet studied this: f is Riemann integrable there since it is bounded and the set of points of discontinuities of f in [0,1] (which is one single point) has (Borel-Lebesgue) measure zero.

Tonio - Nov 2nd 2009, 08:11 PMxyz
As seen above is the graph of the function that has to be proven, it is riemann integrable. So this is how i answered. Please let me know if it is correct --

http://i291.photobucket.com/albums/l...9/Capture2.jpg

http://i291.photobucket.com/albums/l...9/Capture3.jpghttp://i291.photobucket.com/albums/l...9/Capture4.jpg