例3.设f(x)∈C[-a,a], 偶倍奇零 ().(-x)=f(),则。(x)dx=2」0/(x)dx 2)若f(-x)=-f(x),则f(x)dx=0 ME: f(x)dx=. f(x)dx+f(x)d: 「/()d7+0(x)d令x =0[f(-x)+f(x)dx 20/(x)dx,f(x)=f(x)时 0 f(-x)=-f(x)时 HIGH EDUCATION PRESS 机动目录上页下页返回结例3. 证: (1) 若   − = a a a f x x f x x 0 则 ( )d 2 ( )d = − f x x a a ( )d (2) 若 ( )d = 0 − a a 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 机动 目录 上页 下页 返回 结束 令x = −t =