计算∫0+∞xe-xdx
∫0+∞xe-xdx=limb→+∞∫0bxe-xdx =limb→+∞∫0b(-x)de-x=limb→+∞(-xe-x|0b+∫0be-xdx) =limb→+∞(-be-b-e-x|0b)=limb→+∞(-be-b+1-e-b)=1. (注意此处limb→+∞b/eb=limb→+∞1/eb=0)
计算∫0+∞xe-xdx
∫0+∞xe-xdx=limb→+∞∫0bxe-xdx =limb→+∞∫0b(-x)de-x=limb→+∞(-xe-x|0b+∫0be-xdx) =limb→+∞(-be-b-e-x|0b)=limb→+∞(-be-b+1-e-b)=1. (注意此处limb→+∞b/eb=limb→+∞1/eb=0)