设函数f(x)以2π为周期,它在 [ -pi ,pi ) 上的表达式为 f(x)= {int )_(0)^pi xsin 2xdx,g(0)+s(pi )=dfrac ({pi )^2}(2)-1:-|||-B _(2)=(int )_(0)^pi xsin 2xdx (pi )+s(0)=dfrac ({pi )^2}(2)-dfrac (3)(2)-|||-_(a)=dfrac (1)(-)(int )_(x)^xxsin 2xdx (pi )+g(0)=dfrac ({pi )^2}(underline { )}underline ( )-|||-"xsin2xdx,

例2 设f(x)是周期为2π的周期函数,它在 (-pi ,pi ] 上的表达式为-|||-f(x)= ) -1, -pi lt xleqslant 0

设 (x)=pi x+(x)^2 pi leqslant xlt pi 以2π为周期,当f (x)在 [ -pi ,pi ) 上的傅立叶级数为-|||-dfr

1.f(x)是以周期为2π的周期函数,它在 [ -pi ,pi ) 内的表达式为-|||-f(x)= { (B) -pi 。 (C)0 (D)其他值

3.设f(x)以2 π为周期,它在 [ -pi ,pi ) 上的表达式为 f(x)= ) -1 -x& 0lt xlt pi .-|||-展开成傅立叶

定积分(int )_(0)^dfrac (pi {2)}(e)^xsin xdx的值是(int )_(0)^dfrac (pi {2)}(e)^xsin xdx

设=(int )_(-dfrac {pi )(2)}^dfrac (pi {2)}dfrac (sin x)(1+{x)^2}(cos )^4xdx, =(in

(int )_(0)^dfrac (pi {4)}(tan )^2xdx=1-dfrac (pi )(4) __-|||-__下列式子或叙述不正确的是A.B.设

(int )_(0)^dfrac (pi {2)}xsin xdx= ()-|||-

f(x)= pi ,dfrac {pi )(2)lt xlt pi (D)0

1.下列周期函数f(x)的周期为2π,试将f(x)展开成傅里叶级数,如果f(x)在 [ -pi ,pi )-|||-上的表达式为:-|||-(1) (x)=3(