-π≤x≤0 4.将函数f(x)= 展成傅里叶级数. 0<X≤π 解：4=wd=,k+] fcosmdcodcosd n元 及.=”f))sind=sindx+xsnd]0 ( ) 0 x f x x x     −   =     4.将函数 展成傅里叶级数. 解： 0 0 0 1 1 3 ( ) [ ] 2 a f x dx dx xdx         − − = = + =    0 0 1 1 ( ) cos [ cos cos ] n a f x nxdx nxdx x nxdx        − − = = +    0 0 0 2 1 1 1 sin sin cos nx x nx nx n n n      = + + − 2 1 [( 1) 1] n n  = − − 0 0 1 1 ( ) sin [ sin sin ] n b f x nxdx nxdx x nxdx        − − = = +    1 n = − 2 1 3 ( 1) 1 1 ( ) cos sin 4 n n f x nx nx n n    =   − − = + −     