∫(0,1)xf(x)dx
=1/2*∫(0,1)f(x)d(x^2)
=1/2*[f(x)x^2|(0,1) - ∫(0,1)x^2*f'(x)dx]
=-∫(0,1)xsin(x^2)dx
=-1/2*∫(0,1)sin(x^2)d(x^2)
=1/2*cos(x^2)|(0,1)
=1/2*(cos1-1)
这道微积分中的f(x)怎么求啊?
∫(0,1)xf(x)dx
=1/2*∫(0,1)f(x)d(x^2)
=1/2*[f(x)x^2|(0,1) - ∫(0,1)x^2*f'(x)dx]
=-∫(0,1)xsin(x^2)dx
=-1/2*∫(0,1)sin(x^2)d(x^2)
=1/2*cos(x^2)|(0,1)
=1/2*(cos1-1)