王王 F例8设f(x)在,元上连续,证明: IsDx n T /(Sin x) dx 201+c0s2x 证令x=π-t,d=-dt, 左边 0(兀-t)f(sint (一d)= (兀-x)f(sinx I 1+cos t 1+cos- x nITA(sin x) d xf(sinx 0 1+cos x 0 1+cos- x 即2〔"y(snx)=元Cf(mnx) 0 1+cos- x 0 1+cosx sf(sin x) 2dx πr∫(sinx d Jo 1+cosx 2 J0 1+cos x 高等数学(XJD) ▲u高等数学（XJD） . 1 cos (sin ) 1 cos 2 (sin ) ( ) [0, ] , : 0 2 0 2    +  = +  dx x f x dx x xf x 设 f x 在 上连续 证明 证 令 x =  − t, ( ) 1 cos 0( ) (sin ) 2 dt t t f t − +  − =  左边 dx = −dt, dx x x f x   +  − = 0 2 1 cos ( ) (sin ) 例8 dx x xf x dx x f x     + − + =  0 2 0 2 1 cos (sin ) 1 cos (sin ) dx x f x dx x xf x     + =  + 0 2 0 2 1 cos (sin ) 1 cos (sin ) 即 2 . 1 cos (sin ) 1 cos 2 (sin ) 0 2 0 2 dx x f x dx x xf x     +  = + 