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walters

  • 2 years ago

compute the following integral

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  1. walters
    • 2 years ago
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    \[ \int\limits_{\pi}^{\pi}\frac{ 1}{ 1+e ^{sinx} }dx\]

  2. cluo
    • 2 years ago
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    its from pi to pi?

  3. walters
    • 2 years ago
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    oh from -pi to pi

  4. walters
    • 2 years ago
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    i only have the finaly answer (pi) but i don'tknow did they it

  5. cluo
    • 2 years ago
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    what level is this?

  6. walters
    • 2 years ago
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    second

  7. cluo
    • 2 years ago
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    second what?

  8. walters
    • 2 years ago
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    ok maybe i don't understand u which level are u refering to?

  9. cluo
    • 2 years ago
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    which grade?

  10. walters
    • 2 years ago
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    advanced calculus

  11. cluo
    • 2 years ago
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    past vector calculus?

  12. walters
    • 2 years ago
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    i did pure calculus now is the second level of it (which is advanced calculus)

  13. cluo
    • 2 years ago
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    have you done double and triple integrals? i only ask because i think i saw something similar a couple days ago.

  14. walters
    • 2 years ago
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    i am not sure whether this is possible The substitution of x=-y yields |dw:1360491262699:dw| NB:not sure

  15. walters
    • 2 years ago
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    @phi pls help

  16. hartnn
    • 2 years ago
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    do you know a standard integral... \(\int \limits_a^b f(x)dx =\int \limits_a^b f(a+b-x)dx \)

  17. hartnn
    • 2 years ago
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    *standard property.

  18. walters
    • 2 years ago
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    no

  19. hartnn
    • 2 years ago
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    ok, then do you want to use this (1 method) or continue with what u did (another method) of putting x=-y...

  20. walters
    • 2 years ago
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    any method u know u can use it i'll try to catch up

  21. hartnn
    • 2 years ago
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    ok, i'll tell u both, first using your substitution x=-y, |dw:1360492675542:dw| |dw:1360492681874:dw| understood till here ?

  22. walters
    • 2 years ago
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    ok this means i will have |dw:1360492779070:dw| @hartnn can u pls teach me/explain standard property

  23. hartnn
    • 2 years ago
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    yes, you got it correct using your method, now the standard property... let I = integral ..... -------->(1) now using that property, first tell what is a+b-x =.... ?

  24. walters
    • 2 years ago
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    pi-pi-x=-x

  25. hartnn
    • 2 years ago
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    yes, so, because of that property, |dw:1360493289196:dw| add 1 and 2 what u get ?

  26. walters
    • 2 years ago
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    |dw:1360493238315:dw|

  27. walters
    • 2 years ago
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    from -pi to pi

  28. hartnn
    • 2 years ago
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    umm...not actually.... |dw:1360493484296:dw| |dw:1360493501827:dw| s = sin x

  29. hartnn
    • 2 years ago
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    |dw:1360493565788:dw|

  30. hartnn
    • 2 years ago
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    got that ^ ?

  31. walters
    • 2 years ago
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    wow i see now so tell me how wil i know that i must use standart property

  32. hartnn
    • 2 years ago
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    thats trial and error, i first thought of substitution, then recalled different properties, then this property was found to be useful...wih enough practice, this procedure becomes easy and fast...

  33. hartnn
    • 2 years ago
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    also you must know all the properties beforehand ...

  34. walters
    • 2 years ago
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    ok thnx

  35. hartnn
    • 2 years ago
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    welcome ^_^

  36. walters
    • 2 years ago
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    @jacobian see this

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