例3计算定积分 e2+Inx 解 e2+Inx X (2+In xd(2+In x =(2+hx)2 5 2 2 注意凑元不必换限
1 2 ln d . e x x x + 1 (2 ln )d(2 ln ) e = + + x x e x 1 2 (2 ln ) 2 1 = + 例3 计算定积分 解 1 2 ln d e x x x + . 2 5 = 注意:凑元不必换限
例4设函数f()在区间-a,a连续,证明 ()若/(-x)=(x,则∫。fx)dx=2J(xdx (2若(x)=(则(dx=0 IE/(x)dx=f(x)dx+of(x)dx =/(-1d+f(x)dx3 X= LIfGx)+f(x)]dx 20/(x)dx,f(-x)=f(x)时 0 f(-x)=-f(x)时 ▲区鸟
例4 证 (1) 若 f ( − x ) = f ( x ), 0 ( ) d 2 ( ) d a a a f x x f x x − = = − f x x aa ( ) d (2) 若 f ( − x ) = − f ( x ), ( ) d 0 aa 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 = − + 2 ( )d , 0 f x x a f (−x) = f (x)时 0 , f (−x) = − f (x)时令x = −t = 设函数f (t)在区间[− a,a]上连续，证明： 则则