Question

Fourier serie for f(x)=3x^2-2x in -pi 13 years ago

Answer 1

i hope u know the formulas ?

Answer 2

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

Answer 3

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

Answer 4

an and bn exist before cosx and sinx

Answer 5

yea with oyler formula!

Answer 6

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

Answer 7

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

Answer 8

∫−ππ(3x2)d-∫−ππ(2x)d=...? yea?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

a0 = 2(pi)^2

Answer 15

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

Answer 16

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

Answer 17

we should use this state i think!

Answer 18

@hartnn what about other parts?!

Answer 19

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

Answer 20

Some good questions being asked today :)

Answer 21

@abb0t good solution is need for these lol

Answer 22

why don't u try by yourself ?

Answer 23

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

Answer 24

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

Answer 25

final step u got ?

Answer 26

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!

Answer 27

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

Answer 28

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

Answer 29

did u miss 1/pi in the beginning ?

Answer 30

2/pi i missed in beginning! sry

Answer 31

so u having trouble with integration by parts ?

Answer 32

Fractional integrals is needed to solve this?

Answer 33

fractional integers ? no...

Answer 34

so how can u find the that integration?!

Answer 35

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

Answer 36

here u=x^2 , v = cos nx

Answer 37

uv-∫vdu u mean this?

Answer 38

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

Answer 39

actually dv=cosnx and v=-sinnx

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

ok.