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Math Help - Improper integrals

  1. #1
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    Improper integrals

    can someone please explain to me step by step what I am supposed to do? I'm very confused at the moment. thanks for any help.

    Evaluate the integral:
    the integral from 1 to infinity of dx/(x^1.001)
    Last edited by turtle; January 23rd 2007 at 11:44 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by turtle View Post
    can someone please explain to me step by step what I am supposed to do? I'm very confused at the moment. thanks for any help.

    Evaluate the integral:
    the integral from 1 to infinity of dx/(x^1.001)
    You are asked for:

    \int_1^{\infty}\frac{1}{x^{1.001}}dx

    which by the standard rules for the integral of a power other than -1:

    \int_1^{\infty}\frac{1}{x^{1.001}}dx=\left[ -\frac{1}{0.001}\,\frac{1}{x^{0.001}}\right]_1^{\infty}=1000

    RonL
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  3. #3
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    Quote Originally Posted by turtle View Post
    can someone please explain to me step by step what I am supposed to do? I'm very confused at the moment. thanks for any help.

    Evaluate the integral:
    the integral from 1 to infinity of dx/(x^1.001)
    $ is integral

    $ x^-1.001 dx = x^-0.001/0.001 should apply limit

    = (1^-0.001/0.001) - (1/infinite)
    = 1/0.001 - 0
    = 1000
    1000 is right answer.

    R.Mangalesh
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