x≠(2k+1)时∫(x)是以2π为周期的奇函数, 和函数图象 图-3m-2元-7 元/2兀3mx 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
So f(x)sin ndx==5o sinne T cosn,snm兀 +2-n =--coSn兀=-(-1) n+1 (n=1,2,) f(x)=2(sin- sin 2x +sin 3x-.) 3 n+1 ∑ SInn (-∞<x<+0;x≠士π,土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, )