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After taking the antiderivative of lnx what do you do?

I took the derivative of lnx and came up with xlnx-x ], 0<x<1. But since x cannot be 0 in lnx. What do you do?

1 Answer

  • 1 decade ago
    Favorite Answer

    The derivative of ln(x) is 1/x

    The antiderivative of ln(x) is x*ln(x) - x (you got this part right)

    If you want to evaluate this on the interval [0,1] you will need to know the limit of x*ln(x) as it approches 0 from the right. Using L'Hopital's rule, this limit is 0 (see the link below for more details)

    The rest of this evaluation looks like this:

    x*ln(x)-x ] 0<x<1

    (1*ln(1)-1) - (0-0) = -1-0 = -1

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