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mahmit2012

  • 2 years ago

Q6 Find out the integral of log(sinx) in interval (0,pi/2].

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  1. mahmit2012
    • 2 years ago
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    |dw:1337620249282:dw|

  2. akamushi
    • 2 years ago
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    -1.08879

  3. mahmit2012
    • 2 years ago
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    solve it without calculator !!

  4. akamushi
    • 2 years ago
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    integral log(sin(x)) dx = 1/2 i (x^2+Li_2(e^(2 i x)))-x log(1-e^(2 i x))+x log(sin(x))+constant

  5. akamushi
    • 2 years ago
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    then just plug in your interval

  6. mahmit2012
    • 2 years ago
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    are you sure? Ok check it out and then compare with your number.I think that is not true.

  7. akamushi
    • 2 years ago
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    this is a difficult integrand, perhaps i don't remember a short cut. i doubt an instructor would ask this question with out one, especially at lower level calculus.

  8. akamushi
    • 2 years ago
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    i am sure of my anwser.

  9. mahmit2012
    • 2 years ago
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    ok please write your formula in a blank I check it out myself and will show you it is not correct.because there is no close function for this integral.

  10. experimentX
    • 2 years ago
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    i presume you are not looking for numerical methods

  11. mahmit2012
    • 2 years ago
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    yes especially for this interval we have an interesting way to find it out at regular calculus.

  12. experimentX
    • 2 years ago
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    is it approximate value??

  13. experimentX
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=cos+x+plot+from+0+to+pi%2F2 http://www.wolframalpha.com/input/?i=cos+x+plot+from+0+to+pi%2F2 they both seem similar !!

  14. mahmit2012
    • 2 years ago
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    no there is an exact value.i will show you next time.

  15. experimentX
    • 2 years ago
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    something interesting about http://www.wolframalpha.com/input/?i=integrate+x+cotx+from+0+to+pi%2F2

  16. experimentX
    • 2 years ago
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    this seems to give the same result http://www.wolframalpha.com/input/?i=integrate+x^2+cosec^2x%2F2+from+0+to+pi%2F2

  17. mahmit2012
    • 2 years ago
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    |dw:1337635891842:dw|

  18. mahmit2012
    • 2 years ago
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    |dw:1337636241613:dw|

  19. mahmit2012
    • 2 years ago
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    |dw:1337636756218:dw|

  20. mahmit2012
    • 2 years ago
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    |dw:1337636884325:dw|

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