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Math Help - integral

  1. #1
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    integral

    How to integrate sin(x)-log(x) within the limit 0 to 2? What is the value of the integral?

    I am facing problem as log(x) is not defined at x=0.

    Please help
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: integral

    Quote Originally Posted by Suvadip View Post
    I am facing problem as log(x) is not defined at x=0.
    \int_0^2\log x\;dx=\lim_{\epsilon \to 0^+}\int_{\epsilon}^2\log x\;dx .
    Thanks from sbhatnagar
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  3. #3
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    Re: integral

    Thanks for your hint. But does the integral possess any definite value?
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  4. #4
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    Re: integral

    Sure. Have you evaluated \int_\epsilon ^ 2 \log x\ dx in terms of \epsilon?

    Then just consider the limit of that as \epsilon goes to zero.
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  5. #5
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    Re: integral

    Thanks.

    Actually I need to evaluate [tex]\int_)^2 sin(x)-log(x)\dx[\tex] using Trapezoidal rule. I am facing problem as the integrand is not defined at [tex]x=0[\tex]. How to overcome this ?

    Quote Originally Posted by tom@ballooncalculus View Post
    Sure. Have you evaluated \int_\epsilon ^ 2 \log x\ dx in terms of \epsilon?

    Then just consider the limit of that as \epsilon goes to zero.
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