例6设f(x)∈C[-a,a, 偶倍奇零 (I)若f(-)=f(),则，f(x)dr=20f(x)dr 2)若f(-x)=-f(x),则“f(x)dxr=0 证：9fx)dr=〔0，fx)dr+0f(x)dr =∫6f-)dt+j0fx)d 令x=-i =If(-x)+f(x)]dx 20f(x)dr,f-x)=fx)时 0 f(-x)=-f(x)时 例 6 证 : (1) 若   − = a a a f x x f x x 0 则 ( )d 2 ( )d = − f x x aa ( )d (2) 若 ( )d = 0 −aa 则 f x x f x x a ( ) d 0 − f x x a ( ) d 0  + f t t a ( ) d 0  = − f x x a ( ) d 0  + f x f x x a[ ( ) ( )]d 0 = − + f (−x) = f (x)时 f (−x) = − f (x)时 偶倍奇零 令 x = − t =