Question Number 100966 by mhmd last updated on 29/Jun/20

find the fourier series of the function  f(x)= { ((x         −2≤x≤0)),((x+2        0≤x≤2)) :}      help me sir ?

Commented bybobhans last updated on 29/Jun/20

f(x) = (a_o /2) + Σ_(n=1) ^∞  b_n cos (((nπx)/L))  b_n =(2/4) [ ∫_(−2) ^0 x sin (((nπx)/4)) dx + ∫_0 ^2 (x+2)sin (((nπx)/4)) dx ]  b_n = (1/2)[ ∫_(−2) ^2 x sin (((nπx)/4)) dx + ∫_0 ^2 2 sin (((nπx)/4)) dx ]  b_n  = (1/2)[ −((4x)/(nπ)) cos (((nπx)/4))+((16)/((nπ)^2 )) sin (((nπx)/4)) ]_(−2) ^2   − (1/2) [ (8/(nπ)) cos (((nπx)/4)) ]_0 ^2

Commented bymhmd last updated on 29/Jun/20

how are you sir ? am dont anderstand how [bn cos(((nπx)/L))]   because the fourier series is given by   f(x)=((ao)/2)+some (n≥1)[an cos(((nπx)/L))+bn sin(((nπx)/l))]  how bn cos(((nπx)/L)) and where an cos(((nπx)/L)) blease sir can you exact this blease  im very want this equestion ?

Commented bymathmax by abdo last updated on 29/Jun/20

sir bobhans you have supposed that f is even and this is not given in the  question you must use f(x) =(a_o /2) +Σ_(n=1) ^∞  (a_n cos(nwx) +b_n sin(nwx))  a_n =(1/T)∫_(−(T/2)) ^(T/2)  f(x)cos(nx)dx and b_n =(1/T)∫_(−(T/2)) ^(T/2)  f(x)sin(nx)dx   (w =((2π)/T))