例5当(x)在[-a,a上连续,且有 (1)x)为偶函数,则f(x)d=2f(xMtx (2)(x)为奇函数则f(x)dx=0 证1∫。(xx=。f(xM+(xM 在「f(x)k中令x=-t f(x)x=-f(-)=f(-o)t例5 当f(x)在[−a, a]上连续,且有 f x dx f x dx a a  a  = − 0 ( ) 2 ( ) ( ) = 0 − f x dx a a [证] f x dx f x dx f x dx a a a  a   = + − − 0 0 ( ) ( ) ( ) 在 f x dx −a 0 ( ) 中令x= −t f t dt a = − − 0 f x dx ( ) −a 0 ( ) f t dt a  = − 0 ( ) (1)f(x)为偶函数,则 (2)f(x)为奇函数,则