## Hr.Tboy 2 years ago Fourier serie for f(x)=3x^2-2x in -pi<x<pi period!?

1. hartnn

i hope u know the formulas ?

2. Hr.Tboy

$a0+\sum_{1}^{\infty}_{n}cosnx+_{n}sinnx$

3. hartnn

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

4. Hr.Tboy

an and bn exist before cosx and sinx

5. Hr.Tboy

yea with oyler formula!

6. hartnn

$$\large a_0=(1/\pi)\int \limits_{-\pi}^{\pi}(3x^2-2x)dx=....?$$

7. Hr.Tboy

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

8. Hr.Tboy

∫−ππ(3x2)d-∫−ππ(2x)d=...? yea?

9. hartnn

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

10. hartnn

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

11. hartnn

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

12. Hr.Tboy

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

13. hartnn

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

14. JoãoVitorMC

a0 = 2(pi)^2

15. hartnn

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

16. Hr.Tboy

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

17. Hr.Tboy

we should use this state i think!

18. Hr.Tboy

19. hartnn

to find an and bn, you can use integration by parts. try it...if u get stuck, i'll help.

20. abb0t

Some good questions being asked today :)

21. Hr.Tboy

@abb0t good solution is need for these lol

22. hartnn

why don't u try by yourself ?

23. hartnn

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

24. Hr.Tboy

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

25. hartnn

final step u got ?

26. Hr.Tboy

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

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

28. Hr.Tboy

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

29. hartnn

did u miss 1/pi in the beginning ?

30. Hr.Tboy

2/pi i missed in beginning! sry

31. hartnn

so u having trouble with integration by parts ?

32. Hr.Tboy

Fractional integrals is needed to solve this?

33. hartnn

fractional integers ? no...

34. Hr.Tboy

so how can u find the that integration?!

35. hartnn

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

36. hartnn

here u=x^2 , v = cos nx

37. Hr.Tboy

uv-∫vdu u mean this?

38. hartnn

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

39. Hr.Tboy

actually dv=cosnx and v=-sinnx

40. hartnn

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

41. hartnn

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

42. Hr.Tboy

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

43. hartnn

ok.