tag:blogger.com,1999:blog-9004452969563620551.post3253364980854166160..comments2018-09-18T12:34:27.340+05:30Comments on Paramanand's Math Notes: The Riemann Integral: Part 2testernoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-9004452969563620551.post-55816924521105524312018-02-25T11:34:06.797+05:302018-02-25T11:34:06.797+05:30@Unknown,
I have mentioned that $f$ is integrable...@Unknown,<br /><br />I have mentioned that $f$ is integrable on $[a, b] $ and is continuous at some point $c$. Continuity in the entire interval $[a, b] $ is not assumed. So we do need to assume integrability. I hope this clarifies your doubt.<br /><br />Regards,<br />ParamanandParamanand Singhhttps://www.blogger.com/profile/03855838138519730072noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-56827538026038708922018-02-23T03:36:56.939+05:302018-02-23T03:36:56.939+05:30In the "Fundamental theorem of calculus"...In the "Fundamental theorem of calculus" part, in the beginning, you say "if a function f is integrable on [a,b]" and then later you say "provided that f is continuous at c". Why do you include the condition of integrabilty when if f is continuous implies that f is integrable? Or I'm missing something?Unknownhttps://www.blogger.com/profile/09897630187687515374noreply@blogger.com