Shwet Goyal posted an Question
October 09, 2021 • 06:16 am 30 points
  • IIT JAM
  • Mathematics (MA)

Please prove the question by explaining the things

Please prove the question by explaining the things. This is the question from Reimann integral.

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    Kanika goswami 1 best-answer

    check it

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    please tell , why we put in mr and Mr sub-interval value same in f(x) because Mr= f(xr)= cos(rπ÷4n).

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    and if it is due to rational and irrational , then please explain me.

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    mr is for infimum and Mr is for superimum for lower and upper sum calculations....ok

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    upper integral and lower integral is always calculated like this which has done in this question

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    The sub-interval are [(r-1)π/4n, rπ/4n] so, mr will be sin(r-1)π/4n that's right but for Mr must be Cos(r-1)π/4n and here written is Cos(r-1)π/4n.

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    which is wrong in this given solution.

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    because sinx gives minimum and Cosx gives maximum at the same point...that's why we choose value at the same point....ok

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    I hope you will now understand.

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    Ok, thankyou mam , now I understand.

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