- #1
steven187
- 176
- 0
hello all
well I was working through Riemanns Criterion :
let f be a bounded function on the closed interval [a,b]. then f is riemann integrable on [a,b] if and only if , given any epsilon>0, there exist a partition P of [a,b] such that U(f,P)-L(f,P)<epsilon
but there is one thing that I am confused about, riemanns integrability only requires a function to be bounded on a closed interval, if that is the case a piecewise function or a function that is discontinuous at a point which are bounded on a closed interval should be riemann integrable would that be be correct? i just couldn't see how you would intergrate such functions
steven
well I was working through Riemanns Criterion :
let f be a bounded function on the closed interval [a,b]. then f is riemann integrable on [a,b] if and only if , given any epsilon>0, there exist a partition P of [a,b] such that U(f,P)-L(f,P)<epsilon
but there is one thing that I am confused about, riemanns integrability only requires a function to be bounded on a closed interval, if that is the case a piecewise function or a function that is discontinuous at a point which are bounded on a closed interval should be riemann integrable would that be be correct? i just couldn't see how you would intergrate such functions
steven