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

来源:学生作业帮助网 编辑:作业帮 时间:2024/08/01 22:19:04
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
x){n_F9+ubzku45m44m t|miqF@Ov%=ؐ|m]}:O;fUTLKS٧Kf=0QPHIPY@EOȵI*ҧ`AfiǬmRأSR*l55A) 8#@ pS*t^u)#Ovt9>[uz/:]l @~

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