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F ind the value of int0^1logx dxdot...

F ind the value of `int_0^1logx dxdot`

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`I=int_(0)^(1) log xdx=x logx|_(0)^(1)-int_(0)^(1)1dx`
`=1xxlog1-(lim_(xto0)x log x)-1`
`=0-lim_(xto0)(logx)/(1/x)-1`
`=-lim_(xto0)(1/x)/(-1/(x^(2)))-1` (Using L Hopital's rule)
`=lim_(xto0)(x-1)=-1`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
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