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experimentX

  • 2 years ago

find the shortest method to evaluate this \[ \int \frac{\sin x}{\sin x + \cos x} \; dx\]

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  1. siddhantsharan
    • 2 years ago
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    |dw:1347566427407:dw|

  2. experimentX
    • 2 years ago
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    yeah that it is.

  3. siddhantsharan
    • 2 years ago
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    Do you know anything shorter?

  4. experimentX
    • 2 years ago
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    nope ... haven't found any other.

  5. experimentX
    • 2 years ago
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    just noted how similar these two integrals look like \[ \int \frac{\sin x}{\sin x + \cos x} \; dx \\ \int \frac{\cos x}{\sin x + \cos x} \; dx \]

  6. siddhantsharan
    • 2 years ago
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    Note one more way. Although the same really, |dw:1347566670806:dw|

  7. mukushla
    • 2 years ago
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    2I=pi/2 :)

  8. siddhantsharan
    • 2 years ago
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    ^^ No limits here.

  9. experimentX
    • 2 years ago
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    well ... pretty clever manipulation on the last problem

  10. mukushla
    • 2 years ago
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    lol i thought there are ;)

  11. experimentX
    • 2 years ago
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    yeah ... that is also very nice problem. i wish this one had too http://math.stackexchange.com/questions/198083/integrate-sin3x-sin3x-cos3x/198122#198122

  12. experimentX
    • 2 years ago
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    interesting technique ...

  13. siddhantsharan
    • 2 years ago
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    maybe it does. |dw:1347567374847:dw|

  14. siddhantsharan
    • 2 years ago
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    For 2, Taking six + cosx as t, |dw:1347567485586:dw|

  15. experimentX
    • 2 years ago
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    this is just a back hack

  16. siddhantsharan
    • 2 years ago
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    back hack?

  17. experimentX
    • 2 years ago
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    find the answer first ... differentiate the answer to get the get the middle portion.

  18. siddhantsharan
    • 2 years ago
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    How do you find the answer first?

  19. experimentX
    • 2 years ago
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    make it easy as much a possible ... that's how i approach most of the problems. i to honest ... i can't work without answer.

  20. siddhantsharan
    • 2 years ago
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    Okay. Back hack, eh. Hmmmm.

  21. experimentX
    • 2 years ago
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    Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.

  22. siddhantsharan
    • 2 years ago
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    Agreed.

  23. experimentX
    • 2 years ago
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    well ... good night!!

  24. siddhantsharan
    • 2 years ago
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    Yeah. Goodnight. I'll think about this and get back to you tommorow. :)

  25. siddhantsharan
    • 2 years ago
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    Hold onn. What about the current solution to that, It does work quite easily or not?

  26. siddhantsharan
    • 2 years ago
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    To the sin^3x/sin^3x + cos^3x

  27. experimentX
    • 2 years ago
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    there isn't nice manipulation like sin(x)/sin(x)+cos(x) for this one.

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