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Math Help - a question involving definite integral of a ln absolute function?

  1. #1
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    a question involving definite integral of a ln absolute function?

    hello! I have a question regarding an integral which

    int ln(abs(x-1)) dx from 0 to 1

    I know that this can be written as int ln(1-x) dx from 0 to 1
    I try solving the question but I always obtain and undefined function. Any tips on how to solve this question?

    Thanks in advance!
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  2. #2
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    Rewrite it as \int_{ - 1}^0 {\ln (|u|)du} .

    Note that \int {\ln (|u|)du = u\ln (|u|) - u}

    But take care: that is an improper integral. So use limits.
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  3. #3
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    is there a way to do it without improper integrals because we didn't learn those yet.
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  4. #4
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    Quote Originally Posted by Solid8Snake View Post
    is there a way to do it without improper integrals because we didn't learn those yet.
    No. And that being the case, I suggest you wait until after you have been taught about improper integrals before attempting the question. (Of course, you can always self-learn by reading ahead in the textbook)
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