例3.设f(x)∈C[-a,a, 偶倍奇零 (I)若f(-)=f(),则，f()dr=20fx)dx 2)若f(-)=-f(),则f(x)dx=0 证：nfx)dr=,fex)dr+j0fx)dr -Jof(-)di+of()dx 令x=-t =∫Lf(-x)+f(x)]dx L了20f(x)dr,f-x)=fx)时 =10, f(-x)=-f(x)时 oao⊙o&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 =