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Hr.Tboy

  • 2 years ago

Fourier serie for f(x)=3x^2-2x in -pi<x<pi period!?

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  1. hartnn
    • 2 years ago
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    i hope u know the formulas ?

  2. Hr.Tboy
    • 2 years ago
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    \[a0+\sum_{1}^{\infty}_{n}cosnx+_{n}sinnx\]

  3. hartnn
    • 2 years ago
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    wow... anyways, could u find a0 =... ?

  4. Hr.Tboy
    • 2 years ago
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    an and bn exist before cosx and sinx

  5. Hr.Tboy
    • 2 years ago
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    yea with oyler formula!

  6. hartnn
    • 2 years ago
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    \(\large a_0=(1/\pi)\int \limits_{-\pi}^{\pi}(3x^2-2x)dx=....?\)

  7. Hr.Tboy
    • 2 years ago
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    euler formula! bn and an are determined with euler formula too.

  8. Hr.Tboy
    • 2 years ago
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    ∫−ππ(3x2)d-∫−ππ(2x)d=...? yea?

  9. hartnn
    • 2 years ago
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    i don't know how we use euler here, i would integrate by parts for an and bn

  10. hartnn
    • 2 years ago
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    u go on,and tell what u finally get for a0=....?

  11. hartnn
    • 2 years ago
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    yes, its 1/2 pi i thought he wrote a0/2 in the formula, which i generally do.

  12. Hr.Tboy
    • 2 years ago
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    for find the a0 , u should separate ∫(3x2−2x)d to two ∫(3x2)dx-∫2x)dx.

  13. hartnn
    • 2 years ago
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    yeah, that was correct...what u got a0 finally ?

  14. JoãoVitorMC
    • 2 years ago
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    a0 = 2(pi)^2

  15. hartnn
    • 2 years ago
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    \(\large a_0=(1/2\pi)\int \limits_{-\pi}^{\pi}(3x^2-2x)dx=(1/2\pi)[x^3-x^2]^{\pi}_{-\pi}\)

  16. Hr.Tboy
    • 2 years ago
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    3x^2 is an even function. and other one is Individual function.

  17. Hr.Tboy
    • 2 years ago
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    we should use this state i think!

  18. Hr.Tboy
    • 2 years ago
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    @hartnn what about other parts?!

  19. hartnn
    • 2 years ago
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    to find an and bn, you can use integration by parts. try it...if u get stuck, i'll help.

  20. abb0t
    • 2 years ago
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    Some good questions being asked today :)

  21. Hr.Tboy
    • 2 years ago
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    @abb0t good solution is need for these lol

  22. hartnn
    • 2 years ago
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    why don't u try by yourself ?

  23. hartnn
    • 2 years ago
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    we'll correct u if u get it wrong..

  24. Hr.Tboy
    • 2 years ago
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    i tried on paper, it is so long to type here. :D

  25. hartnn
    • 2 years ago
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    final step u got ?

  26. Hr.Tboy
    • 2 years ago
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    i separated that integration to two integration and find a0 an and bn for each of them. so sum them. and after that put it in initial formula!

  27. hartnn
    • 2 years ago
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    what u got a0=...?an=...?bn=...?

  28. Hr.Tboy
    • 2 years ago
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    an for first integration is this: an=\[\int\limits_{0}^{\pi}3x^{2}cosnxdx \rightarrow......?\]

  29. hartnn
    • 2 years ago
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    did u miss 1/pi in the beginning ?

  30. Hr.Tboy
    • 2 years ago
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    2/pi i missed in beginning! sry

  31. hartnn
    • 2 years ago
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    so u having trouble with integration by parts ?

  32. Hr.Tboy
    • 2 years ago
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    Fractional integrals is needed to solve this?

  33. hartnn
    • 2 years ago
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    fractional integers ? no...

  34. Hr.Tboy
    • 2 years ago
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    so how can u find the that integration?!

  35. hartnn
    • 2 years ago
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    didn't u try integration by parts ? u know what that is, right ? \(\int uv = ... ?\)

  36. hartnn
    • 2 years ago
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    here u=x^2 , v = cos nx

  37. Hr.Tboy
    • 2 years ago
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    uv-∫vdu u mean this?

  38. hartnn
    • 2 years ago
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    yes. u = x^2 what will u take dv =... ?

  39. Hr.Tboy
    • 2 years ago
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    actually dv=cosnx and v=-sinnx

  40. hartnn
    • 2 years ago
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    yes, yes, go ahead and solve it...

  41. hartnn
    • 2 years ago
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    you'll again need product rule when u solve for sin nx (2x)dx

  42. Hr.Tboy
    • 2 years ago
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    yea thnx... i'll try and finally put the answer here to prove;)

  43. hartnn
    • 2 years ago
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    ok.

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