设f(x)在[a,b]上连续,f(a)=f(b)=0,定积分f^2(x)从b到a等于1,则定积分xf(x)f'(x)等于多少A.1/2 B.1 C.0 D.-1/2
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![设f(x)在[a,b]上连续,f(a)=f(b)=0,定积分f^2(x)从b到a等于1,则定积分xf(x)f'(x)等于多少A.1/2 B.1 C.0 D.-1/2](/uploads/image/z/5349643-43-3.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2Cf%28a%29%3Df%28b%29%3D0%2C%E5%AE%9A%E7%A7%AF%E5%88%86f%5E2%28x%29%E4%BB%8Eb%E5%88%B0a%E7%AD%89%E4%BA%8E1%2C%E5%88%99%E5%AE%9A%E7%A7%AF%E5%88%86xf%28x%29f%27%28x%29%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91A.1%2F2+B.1+C.0+D.-1%2F2)
设f(x)在[a,b]上连续,f(a)=f(b)=0,定积分f^2(x)从b到a等于1,则定积分xf(x)f'(x)等于多少A.1/2 B.1 C.0 D.-1/2
设f(x)在[a,b]上连续,f(a)=f(b)=0,定积分f^2(x)从b到a等于1,则定积分xf(x)f'(x)等于多少
A.1/2 B.1 C.0 D.-1/2
设f(x)在[a,b]上连续,f(a)=f(b)=0,定积分f^2(x)从b到a等于1,则定积分xf(x)f'(x)等于多少A.1/2 B.1 C.0 D.-1/2
刚回荅:
∫xf(x)f'(x)dx=(1/2)∫xdf(x)^2=(1/2)xf(x)^2-(1/2)∫f(x)^2dx,代入上下限后=-1/2.选D
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