Riemann Integration | Lecture 27 | Square of Riemann Integrable Function is Riemann Integrable

[@Sameer2023-h3n]

Thnks a lot Sir ❤
Sir pls make a vdo on the theorem
1) "If f is integrable on [a, b] , then f is Integrable on any subinterval [c, d] of [a, b]. "
2) integration a to b fdx= integration a to c fdx + integration c to b fdx, for any c belongs to [a, b]

[@masoudsakha9331]

great thanks

[@aiswaryak7566]

Sir, plz make more videos related to theorems of RS integrable

[@manishpandit3039]

Nice👏👏 teaching sir

[@ranjankhatu]

Thank you very much

[@priyashrideb4981]

Tnq sir

[@guljabinhussain3935]

Sir is the converse of this theorem is true

[@ranjankhatu]

@@guljabinhussain3935 no

[@jiwantika19]

Sir why u have taken here |f| , by using 'f' also it can be proved
Then what is necessity of taking |f|?

[@ranjankhatu]

Yes. It is necessary to take mod f there to get relationship in values of m_i

[@jiwantika19]

Thanku so much sir
Yours teaching style is better than fantastic🤘

[@ranjankhatu]

@@jiwantika19 thank you so much for your comment.

[@subratadas9836]

If f² is integrable does it implie f is integrable?

[@ranjankhatu]

no

[@subratadas9836]

Sir can you give me any example

[@ranjankhatu]

@@subratadas9836value of f is 1 if x is rational and it is -1 if f is irrational. Here f^2 is 1 which is constant and hence integrable but f is not integrable.

[@subratadas9836]

Thanks sir

[@subratadas9836]

And how I proof f³ is integrable

[@蔺美云]

👍👍👍

[@sagarsahu956]

Sir please teach in hindi language