求下列函数的积分,我是菜菜鸟,

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求下列函数的积分,我是菜菜鸟,求下列函数的积分,我是菜菜鸟,求下列函数的积分,我是菜菜鸟,【0,+∞】∫2ye^(-y)dy=【0,+∞】-2∫yd[e^(-y)]=【0,+∞】-2[ye^(-y)-

求下列函数的积分,我是菜菜鸟,
求下列函数的积分,我是菜菜鸟,

求下列函数的积分,我是菜菜鸟,
【0,+∞】∫2ye^(-y)dy=【0,+∞】-2∫yd[e^(-y)]=【0,+∞】-2[ye^(-y)-∫e^(-y)dy]
=【0,+∞】-2[ye^(-y)+∫e^(-y)d(-y)]={-2[ye^(-y)+e^(-y)]}【0,+∞】
=y→+∞lim[-2(y+1)/e^y]+2=y→+∞lim(-2/e^y)+2=2