求积分∫(1~4)(4-x)sin(x-1)dx

∫[1→4] (4-x)sin(x-1) dx=4∫[1→4] sin(x-1) dx-∫[1→4] xsin(x-1) dx=-4cos(x-1) + ∫[1→4] x d(cos(x-1))=-4cos(x-1) + xcos(x-1) - ∫[1→4] cos(x-1)dx=-4cos(x-1) + xcos(x-1) - sin(x-1) |[1→4]=-4cos3 ...