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Homework Help: Intergration problem

  1. Mar 26, 2005 #1
    Hi i am completely stuck on a intergration problem, i have tried substition, and every technique i can think off but i cannot solve it. It is a improper intergral and the answer is pie/4

    The question is:

    find the intergral with limits upper pie/2 and lower 0

    1/(1+(tanx)^sqaureroot pie).dx

    P.S: how do i type equations liek the way some ppl do in their threads
     
  2. jcsd
  3. Mar 26, 2005 #2
    [tex] \int\frac{1}{1+tan^{\sqrt{e\pi}}(x)}{dx} [/tex]

    Is that the right integral? Clicking the graphic will show you the code to type it.
     
  4. Mar 26, 2005 #3
  5. Mar 26, 2005 #4

    dextercioby

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    Okay.Here's the antiderivative

    [tex]\int \frac{dx}{1+\tan^{\sqrt{\pi}} x} [/tex]


    (v.attachement).

    Now,u can see that,both in the lower limit & in the upper one,u need to compute the limits in ivolving the [tex] _{2}F_{1} [/tex] of an adorable argument & tangent of "x" to a weird power.

    Good luck with those limits... :smile:

    Daniel.
     

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  6. Mar 26, 2005 #5
    and by the way, [itex]\pi[/itex] is spelled "pi." :)
     
  7. Mar 26, 2005 #6

    dextercioby

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    I like "pie"...:tongue2:Yumm-Yumm :!!) (Please work on that Latex code,will u?People are confused because of your weird notations).

    Daniel.
     
  8. Mar 26, 2005 #7
    There's also only 1 r in both "integration" and "integral".
     
  9. Mar 26, 2005 #8

    dextercioby

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    And it's "...think of"...:tongue2: And "like" (sic!)...


    Daniel.


    P.S.Another piece of advice:use the spell checker.
     
    Last edited: Mar 26, 2005
  10. Mar 26, 2005 #9
    Its "Another PIECE OF advice" :-D
     
  11. Mar 27, 2005 #10
    Thanks so much guys, wow you guys run a real good service. Oh, and thanks for the correction, of course how stupid was i to write "pie", indeed it is "pi".
     
  12. Mar 27, 2005 #11
    No, this is the integral [tex]\int \frac{dx}{1+\tan^{\sqrt{\pi}} x} [/tex]
    Oh, and to the dexter, could you clarify what steps you took reach the antiderrivative? Like substitution or interation by parts?
     
  13. Mar 27, 2005 #12
    He got mathematica to do it. I find it extremely unlikely that it is possible to express the antiderivative in terms of elementary functions. In what context did this integral appear?
     
  14. Mar 27, 2005 #13
    Oh, so he used a computer program or something? So this integral cannot be expressed with elementary functions?
     
  15. Mar 27, 2005 #14

    dextercioby

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    Well,it cannot.If u decide to include hypergeometric functions among elementary functions,then u might say it is,else,not.

    Now,if u plot the functions

    [tex] \frac{1}{1+\tan^{\sqrt{\pi}}x} [/tex] & [tex] \frac{1}{1+\tan^{2}x} [/tex] on the interval [tex] [0,\frac{\pi}{2}) [/tex]

    ,then,by evaluating the integral of the second function on the same interval (which is very,very easy),u might get an approximation to the first integral.If u have a software that could plot them together in the same picture/graph,it would be perfect.

    Daniel.
     
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