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Thread: vip integral

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    vip integral

    find
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dapore View Post
    find
    It doesn't converge.
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    Quote Originally Posted by Drexel28 View Post
    It doesn't converge.
    Why?
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    Well, if you use integration by parts, regardless of what you get for the other forms in: $\displaystyle \int u*dv = u*v-\int du*v$

    The form of u*v will be undefined for one of your functions.

    Which one and why I leave to you, but it should be obvious if you use IBP. Are you that far yet - you'd have to be to do this problem.
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    Quote Originally Posted by dapore View Post
    find
    Consider

    $\displaystyle f(x)=\frac x{\ln(x)}$

    The domain of this function is $\displaystyle d = [0, 1) \cup (1, \infty)$

    and

    f(x) is approaching $\displaystyle -\infty$ if x approaches 1 from the left;
    f(x) is approaching $\displaystyle +\infty$ if x approaches 1 from the right.

    That's the reason why your integraL cann't exist.
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    I want more clarification, I should be grateful to you
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    Quote Originally Posted by dapore View Post
    I want more clarification, I should be grateful to you
    It's easy:

    1. Draw the graph of $\displaystyle f(x)=\frac x{\ln(x)}$

    2. Draw the borders of the integral and it is obvious that the integral doesn't exist.
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    Quote Originally Posted by dapore View Post
    I want more clarification, I should be grateful to you
    There is absolutely no need for you to screem at us.
    Using size five type is uncalled for.

    Now here is a question for you: "Do you understand an improper integral?"
    Note the function $\displaystyle \frac{x}{\ln(x)}$ is not defined for either $\displaystyle x=0\text{ or }x=1$.
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