x≠(2k+1)π时f(x)是以2π为周期的奇函数, 和函数图象 3 2丌3兀 T 0,(n=0,1,2,…)
− − 3 − 2 − 2 3 x y0 x (2k +1)时 f (x)是以2为周期的奇函数, 和函数图象a = 0, (n = 0,1,2,) n
2 2 b =o f()sin ndx=Jo xsin ndx T x cos r sinn 公2 n coS n n1+1 (n=1,2,) n n f(r=2(sinx-sin 2x+sin 3x -") 3 n+1 2 (-1) SInn n-=1 n (-∞<x<+x≠土π,±3π,…)
= 0 ( )sin 2 bn f x nxdx = 0 sin 2 x nxdx − + = 2 0 ] cos sin [ 2 n nx n x nx = − n n cos 2 ( 1) , 2 +1 = − n n (n = 1,2, ) sin3 ) 3 1 sin2 2 1 f (x) = 2(sin x − x + x − sin . ( 1) 2 1 1 = + − = n n nx n (− x +; x , 3, )