anonymous
  • anonymous
Fourier serie for f(x)=3x^2-2x in -pi
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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hartnn
  • hartnn
i hope u know the formulas ?
anonymous
  • anonymous
\[a0+\sum_{1}^{\infty}_{n}cosnx+_{n}sinnx\]
hartnn
  • hartnn
wow... anyways, could u find a0 =... ?

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anonymous
  • anonymous
an and bn exist before cosx and sinx
anonymous
  • anonymous
yea with oyler formula!
hartnn
  • hartnn
\(\large a_0=(1/\pi)\int \limits_{-\pi}^{\pi}(3x^2-2x)dx=....?\)
anonymous
  • anonymous
euler formula! bn and an are determined with euler formula too.
anonymous
  • anonymous
∫−ππ(3x2)d-∫−ππ(2x)d=...? yea?
hartnn
  • hartnn
i don't know how we use euler here, i would integrate by parts for an and bn
hartnn
  • hartnn
u go on,and tell what u finally get for a0=....?
hartnn
  • hartnn
yes, its 1/2 pi i thought he wrote a0/2 in the formula, which i generally do.
anonymous
  • anonymous
for find the a0 , u should separate ∫(3x2−2x)d to two ∫(3x2)dx-∫2x)dx.
hartnn
  • hartnn
yeah, that was correct...what u got a0 finally ?
anonymous
  • anonymous
a0 = 2(pi)^2
hartnn
  • hartnn
\(\large a_0=(1/2\pi)\int \limits_{-\pi}^{\pi}(3x^2-2x)dx=(1/2\pi)[x^3-x^2]^{\pi}_{-\pi}\)
anonymous
  • anonymous
3x^2 is an even function. and other one is Individual function.
anonymous
  • anonymous
we should use this state i think!
anonymous
  • anonymous
@hartnn what about other parts?!
hartnn
  • hartnn
to find an and bn, you can use integration by parts. try it...if u get stuck, i'll help.
abb0t
  • abb0t
Some good questions being asked today :)
anonymous
  • anonymous
@abb0t good solution is need for these lol
hartnn
  • hartnn
why don't u try by yourself ?
hartnn
  • hartnn
we'll correct u if u get it wrong..
anonymous
  • anonymous
i tried on paper, it is so long to type here. :D
hartnn
  • hartnn
final step u got ?
anonymous
  • anonymous
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
  • hartnn
what u got a0=...?an=...?bn=...?
anonymous
  • anonymous
an for first integration is this: an=\[\int\limits_{0}^{\pi}3x^{2}cosnxdx \rightarrow......?\]
hartnn
  • hartnn
did u miss 1/pi in the beginning ?
anonymous
  • anonymous
2/pi i missed in beginning! sry
hartnn
  • hartnn
so u having trouble with integration by parts ?
anonymous
  • anonymous
Fractional integrals is needed to solve this?
hartnn
  • hartnn
fractional integers ? no...
anonymous
  • anonymous
so how can u find the that integration?!
hartnn
  • hartnn
didn't u try integration by parts ? u know what that is, right ? \(\int uv = ... ?\)
hartnn
  • hartnn
here u=x^2 , v = cos nx
anonymous
  • anonymous
uv-∫vdu u mean this?
hartnn
  • hartnn
yes. u = x^2 what will u take dv =... ?
anonymous
  • anonymous
actually dv=cosnx and v=-sinnx
hartnn
  • hartnn
yes, yes, go ahead and solve it...
hartnn
  • hartnn
you'll again need product rule when u solve for sin nx (2x)dx
anonymous
  • anonymous
yea thnx... i'll try and finally put the answer here to prove;)
hartnn
  • hartnn
ok.

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