Hr.Tboy
Fourier serie for f(x)=3x^22x in pi<x<pi period!?



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hartnn
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i hope u know the formulas ?

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

hartnn
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wow...
anyways, could u find a0 =... ?

Hr.Tboy
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an and bn exist before cosx and sinx

Hr.Tboy
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yea with oyler formula!

hartnn
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\(\large a_0=(1/\pi)\int \limits_{\pi}^{\pi}(3x^22x)dx=....?\)

Hr.Tboy
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euler formula! bn and an are determined with euler formula too.

Hr.Tboy
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∫−ππ(3x2)d∫−ππ(2x)d=...? yea?

hartnn
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i don't know how we use euler here, i would integrate by parts for an and bn

hartnn
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u go on,and tell what u finally get for a0=....?

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

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

hartnn
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yeah, that was correct...what u got a0 finally ?

JoãoVitorMC
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a0 = 2(pi)^2

hartnn
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\(\large a_0=(1/2\pi)\int \limits_{\pi}^{\pi}(3x^22x)dx=(1/2\pi)[x^3x^2]^{\pi}_{\pi}\)

Hr.Tboy
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3x^2 is an even function. and other one is Individual function.

Hr.Tboy
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we should use this state i think!

Hr.Tboy
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@hartnn what about other parts?!

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.

abb0t
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Some good questions being asked today :)

Hr.Tboy
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@abb0t good solution is need for these lol

hartnn
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why don't u try by yourself ?

hartnn
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we'll correct u if u get it wrong..

Hr.Tboy
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i tried on paper, it is so long to type here. :D

hartnn
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final step u got ?

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!

hartnn
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what u got a0=...?an=...?bn=...?

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

hartnn
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did u miss 1/pi in the beginning ?

Hr.Tboy
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2/pi i missed in beginning! sry

hartnn
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so u having trouble with integration by parts ?

Hr.Tboy
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Fractional integrals is needed to solve this?

hartnn
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fractional integers ? no...

Hr.Tboy
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so how can u find the that integration?!

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

hartnn
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here u=x^2 , v = cos nx

Hr.Tboy
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uv∫vdu u mean this?

hartnn
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yes.
u = x^2
what will u take dv =... ?

Hr.Tboy
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actually dv=cosnx and v=sinnx

hartnn
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yes, yes, go ahead and solve it...

hartnn
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you'll again need product rule when u solve for sin nx (2x)dx

Hr.Tboy
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yea thnx... i'll try and finally put the answer here to prove;)

hartnn
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ok.