推论2若f(x)在[ab上连续,1(x)2(x)在[ab上可导, d,1m2(x)g(x)-/(x)q(x dx e(x) 证因/ (x) 1(x) f(t)dt f()dt- f(t)dt q1(x) 则 f(tdt=f[o2(x)] 2(x)-f[,(x)] (x) dx Je(x) 例7计算下列各题 ()o解a∫os:h=csx da Ja 解 d=,(-|ea) dl4 推论2 若ƒ(x)在[a, b]上连续, 1 2   ( ), ( ) x x 2 1 ( ) 2 2 1 1 ( ) ( ) [ ( )] ( ) [ ( )] ( ) x x d f t dt f x x f x x dx   =  −         2 2 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) x x x x c c f t dt f t dt f t dt     = − 因    例7 计算下列各题 2 0 (1) cos d x t dt dx  2 2 0 cos cos d x t dt x dx = 解  证 在[a, b]上可导, 则 2 1 ( ) 2 2 1 1 ( ) ( ) [ ( )] ( ) [ ( )] ( ) x x d f t dt f x x f x x dx   =  −         3 (2) x t a d e dt da  3 x t a d e dt da = 解  3 3 ( ) a t a x d e dt e da − = −  则