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Math Help - comparision test

  1. #1
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    comparision test

    Use a comparison to determine whether the integral converges or diverges:

    A  \int \frac{x^2e^x}{lnx}dx = from 2 to infinite

    This integral diverges , but how can I show that using the comparison test?

    B  \int \frac{1000}{pi^(2x)+x^2}dx =

    it is pi^2x in the denomenator
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  2. #2
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    Quote Originally Posted by Abbas View Post
    Use a comparison to determine whether the integral converges or diverges:

    A  \int \frac{x^2e^x}{lnx}dx = from 2 to infinite

    This integral diverges , but how can I show that using the comparison test?


    We have \frac{x^2e^x}{\ln x}\geq e^x and clearly \int\limits_2^\infty e^x\,dx diverges.

    B  \int \frac{1000}{pi^(2x)+x^2}dx =


    What are the limits here?? \frac{1000}{\pi^2x+x^2}\le \frac{1000}{x^2} , and \int\limits_1^\infty \frac{1000}{x^2}\,dx =\lim_{b\to \infty}-\frac{1000}{b}+1000=1000 , so the integral converges (unless the lower limit is not 1 but something else...)

    Tonio



    it is pi^2x in the denomenator
    .
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  3. #3
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    ThanX alot ..
    the second prblems limits ( 2 , infinite )
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  4. #4
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    Quote Originally Posted by Abbas View Post
    ThanX alot ..
    the second prblems limits ( 2 , infinite )

    It's just the same: the integral still converges as can easily be checked. The problem arises when the lower limit is zero.

    Tonio
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