Question

帮忙求个定积分,

Answer 1

∫(0,1)1/3y^3e^(-y^2)dy

=1/3∫(0,1)y^2*y*e^(-y^2)dy

=1/3∫(0,1)y^2e^(-y^2)dy^2/2

=-1/6∫(0,1)y^2e^(-y^2)d(-y^2)

=-1/6∫(0,1)y^2de^(-y^2)

=-1/6(e^(-y^2)*y^2-∫(0,1)e^(-y^2)dy^2)

=-1/6(e^(-y^2)*y^2+∫(0,1)de^(-y^2))

=-1/6(e^(-y^2)*y^2+e^(-y^2)+C ) (0,1)

=-1/6*e^(-y^2)(y^2+1) +C) (0,1)

=-1/6(e^-1*(1+1)+C-e^0*(0+1)-C)

=-1/6(2/e-1)