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Am i doing this question correctly.

  1. Aug 21, 2011 #1
    1. The problem statement, all variables and given/known data

    The integral of [x]+ln( (1+x)/(1-x) ) (lower limit -0.5 and upper limit is 0.5.)
    here [x] show greater integer function means greatest integer less than equal to x. ex [2.3]=0.3,[1.7]=0.7,[-1.4]=0.6 etc.
    //sorry that i don't know how to write it in better way

    2. Relevant equations

    millions so i can't write all of them here two of them is
    integral of f(x) from a to b =integral of f(a+b-x) from a to b.
    [1-x]=1-[x]
    rest are in your mind.

    3. The attempt at a solution

    replace x by lower limit+ upper limit-x.
    function will changed into [1-x]+ln( (1-x)/(1+x) )
    replace [1-x] with 1-[x]. after little modification it will something like this I=integral with limits(1) -I
    here I is the integral whose value i want to know.
    finally the answer is 1/2 but this is wrong. correct answer as given in book is -1/2. My question is why my answer is wrong?
    thanks for any kind of help.

    vikash chandola
    suport anna hazare(only for indians)
     
    Last edited: Aug 21, 2011
  2. jcsd
  3. Aug 21, 2011 #2
    You have the greatest integer function wrong. example: [2.3]=2
    As for the rest of the problem, I'm not sure how to do it.
     
  4. Aug 21, 2011 #3

    SammyS

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    [itex]\displaystyle \int_{-0.5}^{0.5}\lfloor x \rfloor dx[/itex] should be a piece of cake.
    For -1 ≤ x < 0 , [itex]\displaystyle \lfloor x \rfloor = -1[/itex].

    For 0 ≤ x < 1 , [itex]\displaystyle \lfloor x \rfloor = 0[/itex].​

    For [itex]\displaystyle \ln\left(\frac{1+x}{1-x}\right)\,,[/itex] use the rule for the log of a quotient. Then break-up the integral accordingly.

    Do you know the anti-derivative of ln(x) ?
     
  5. Aug 21, 2011 #4
    Oh man. what a foolish work i did. I understand greater integer function as fraction part function. I also applly wrong property that's why i got wrong answer.After thanks you tel me my mistake.


    Hey sammy what are you writing. this is seeming lengthy method. see how i solve it. thing i do wrong is understand greatest integer function as fraction part function. So the property [-x]=1-[x] is wrong. Correct one is [-x]=-1-[x]. now i will get correct answer.

    anti derivative of ln(x) is xln(x)-x+C
     
  6. Aug 21, 2011 #5

    SammyS

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    The problem has [x]. Why are you working with [-x] ?
     
  7. Aug 24, 2011 #6
    oh one more sorry. Actually the place where i write [1-x] that is [-x] =-1-[x].
    I do this mistake however my trick is correct. thanks for showing me my mistake. If you still say how yo write [-x] then something is wrong. either i am doing one more mistake or you do something wrong.
     
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