例3计算 sin'x-sin xdx. a解'"f(x)=Vsin3x-sim=cosx(sinx)月 sinx-sin"xd=cosx(sinx)de eos (sin )cos(sin )e =j后(6 sin x)dsin-」(sindsinx -g6n时e如- HIGH EDUCATION PRESS
例3 计算 解 sin sin . 0 3 5 x − xdx f x x x 3 5 ( ) = sin − sin ( )2 3 = cos x sin x − 0 3 5 sin x sin xdx ( ) = 0 2 3 cos x sin x dx ( ) = 2 0 2 3 cos x sin x dx ( ) − 2 2 3 cos x sin x dx ( ) = 2 0 2 3 sin x d sin x ( ) − 2 2 3 sin x d sin x ( ) 2 0 2 5 sin 5 2 = x ( ) − 2 2 5 sin 5 2 x . 5 4 =
例4.计算 dx 解令1=2x+1,则x-21dk=1d,且 2 当x=0时，t=1;x=4时，1=3. =e-3)a -3的39号 HIGH EDUCATION PRESS 机动目录上页下页返回结束
例4. 计算 解: 令 t = 2x +1, 则 , d d , 2 1 2 x t t t x = − = 当x = 0时, x = 4时, t = 3. ∴ 原式 = t t t t d 3 2 1 2 1 2 + − (t 3)dt 2 1 3 1 2 = + 3 ) 3 1 ( 2 1 3 = t + t 1 3 t =1; 机动 目录 上页 下页 返回 结束 且
例5.设f(x)eCL-a,a, 偶倍奇零 (1)若f(-x)=fx),则fx)dx=20f(x)d 2)若f(-x)=-f(x),则，f(x)dx=0 证，fw)d=fx山+9f6d =J0f(-)dr+∫fx)d 令x=- =If(-x)+f(x)]dx 。7 f(-x)=-f(x)时 HIGH EDUCATION PRESS 机动目录上页下页返回结束
例5. 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 =