搜搜做题作业网帮忙求个定积分,
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/04/27 08:09:10
帮忙求个定积分,
∫(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)
=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)