讨论广义积分∫【1,0】dx/x^q的敛散性.如题.
问题描述:
讨论广义积分∫【1,0】dx/x^q的敛散性.
如题.
答
∫【1,0】dx/x^q
=【1,0】x^(1-q)/(1-q)
=1/(1-q)-lin(x->0+)x^(1-q)/(1-q)
=1/(1-q)+lin(x->0+)(1/x)^(q-1)/(q-1)
=1+∞
=+∞