b b Cf()dx=Sf(x)dx+5f(x)dx lim f(x)dx+ lim f(x)dx 三、典型例题 T 例1 求 sIn 0 sinx+ cos x 解由/=2 SIn cos d dx,设J dx 0 sinx+cos x o sixt cos x 则/+/=k=y sInx- cos x d (cos x +sin x) 0 sinx+ cos x =0 0 sinx+ cosx T 故得2 即I 2 b a f (x)dx =  c a f (x)dx+  b c f (x)dx  − →+ =   c a lim f (x)dx 0  +  →+ + b c f x dx   lim ( ) 0 三、典型例题 例1 . sin cos sin 2 0  + dx x x x 求 解 , sin cos sin 2 0  + = dx x x x 由 I , sin cos cos 2 0  + = dx x x x 设 J , 2 2 0  + = =   则 I J dx   + − − = 2 0 sin cos sin cos dx x x x x I J   + + = − 2 0 sin cos (cos sin ) x x d x x = 0. , 2 2  故得 I = . 4  即 I =