Let f:[a,b]---->R be Riemann integrable. Define F:[a,b]---->R by F(x)= ii) Prove that F is bounded. F is bounded if |F'|<=f yes? how do we know f is bounded? thanks
Follow Math Help Forum on Facebook and Google+
Originally Posted by charikaar Let f:[a,b]---->R be Riemann integrable. Define F:[a,b]---->R by F(x)= ii) Prove that F is bounded. F is bounded if |F'|<=f yes? how do we know f is bounded? thanks Since : = F(x) +hf(c) ,where x<c<x+h, by the mean value theorem of integrals. Hence Hence F continuous on [a,b] ,thus bounded on [a,b]
Last edited by xalk; Mar 18th 2010 at 08:26 AM. Reason: not complete
View Tag Cloud