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Hr.Tboy

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

  • one year ago
  • one year ago

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  1. hartnn
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    i hope u know the formulas ?

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

    • one year ago
  3. hartnn
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    wow... anyways, could u find a0 =... ?

    • one year ago
  4. Hr.Tboy
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    an and bn exist before cosx and sinx

    • one year ago
  5. Hr.Tboy
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    yea with oyler formula!

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

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

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

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

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

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

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

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

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

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

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

    • one year ago
  17. Hr.Tboy
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    we should use this state i think!

    • one year ago
  18. Hr.Tboy
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    @hartnn what about other parts?!

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

    • one year ago
  20. abb0t
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    Some good questions being asked today :)

    • one year ago
  21. Hr.Tboy
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    @abb0t good solution is need for these lol

    • one year ago
  22. hartnn
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    why don't u try by yourself ?

    • one year ago
  23. hartnn
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    we'll correct u if u get it wrong..

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

    • one year ago
  25. hartnn
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    final step u got ?

    • one year ago
  26. Hr.Tboy
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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!

    • one year ago
  27. hartnn
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    what u got a0=...?an=...?bn=...?

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

    • one year ago
  29. hartnn
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    did u miss 1/pi in the beginning ?

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

    • one year ago
  31. hartnn
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    so u having trouble with integration by parts ?

    • one year ago
  32. Hr.Tboy
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    Fractional integrals is needed to solve this?

    • one year ago
  33. hartnn
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    fractional integers ? no...

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

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

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

    • one year ago
  37. Hr.Tboy
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    uv-∫vdu u mean this?

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

    • one year ago
  39. Hr.Tboy
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    actually dv=cosnx and v=-sinnx

    • one year ago
  40. hartnn
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    yes, yes, go ahead and solve it...

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

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

    • one year ago
  43. hartnn
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    ok.

    • one year ago
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