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 =
二、定积分的分部积分法 定理2.设u(x),v(x)∈Cl[a,b],则 drd-wl2reoe)dr 证：[u(x)v(x)'=u(x)v(x)+u(x)v'(x) 两端在[a,b]上积分 une)l2-acr(d+aumxdr =dntl合aar)r OOo⊙08 机无
二、定积分的分部积分法 定理2. ( ), ( ) [ , ], 1 设u x v x C a b 则 a b 证: [u(x)v(x)] = u (x)v(x) + u(x)v (x) u(x)v(x) a b u x v x x u x v x x b a b a = ( ) ( )d + ( ) ( )d = u(x)v(x) a b − b a u (x) v(x)dx 机动 目录 上页 下页 返回 结束 两端在[a,b]上积分