第五章 定积分 高等数学少学时 例4证明：（1)若f(x)在[4，b]上连续且为偶函数，则 ∫nfx)dc=22fxde (2)若fx)在[，b]上连续且为奇函数，则 f(x)dx=0. 偶倍奇零 证nf(x)dr=∫nf(x)de+J6f(x)x 而∫f(x)d=--∫心f(-)d=f-0=6f-xydx ∴∫，fx)dc=∫if-x)dr+Jfx)de =∫[f-)+fx]d 北京邮电大学出版社 01010 证 0 0 ( )d ( )d ( )d a a a a f x x f x x f x x − − = +   0 ( )d a = − f t t  x = −t ( ) 0 d a − − f t t    0 ( ) ( ) d a = − + f x f x x  0 0 ( )d ( )d ( )d a a a a f x x f x x f x x −  = − +    ( ) 0 d a f x x 而 − 0 ( )d a = − f x x  偶倍奇零 0 ( )d 2 ( )d ; a a a f x x f x x − =   例４ 证明:（1）若 f(x)在[a,b]上连续且为偶函数，则 ( )d 0. a a f x x − =  （2）若 f (x) 在[a, b]上连续且为奇函数，则