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Math Help - Improper integrals

  1. #1
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    Improper integrals

    Hey guys I'm having a little trouble with improper integrals in general and I came here looking for some help. I need to know which integrals are convergent and divergent and which integrals are improper.

    Can someone give me a couple points and tips when dealing with improper integrals.

    An example problem is x^4 e^-x^4 dx l infinity and 1
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  2. #2
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    Re: Improper integrals

    Quote Originally Posted by kashmoneyrecord3 View Post
    Hey guys I'm having a little trouble with improper integrals in general and I came here looking for some help. I need to know which integrals are convergent and divergent and which integrals are improper.

    Can someone give me a couple points and tips when dealing with improper integrals.

    An example problem is x^4 e^-x^4 dx l infinity and 1
    the following link can answer your general questions about improper integrals ...

    Pauls Online Notes : Calculus II - Improper Integrals


    for your specific example, start by noting the following inequality ...

    \int_1^\infty x^4 e^{-x^4} \, dx < \int_1^\infty 4x^7 e^{-x^4} \, dx

    for the larger integral, let t = x^4

    dt = 4x^3 \, dx

    substitute ...

    \int_1^\infty t e^{-t} \, dt

    using integration by parts, it's a fairly simple process to show the convergence of this integral.

    since the improper integral in question is less than this convergent improper integral, by direct comparison they both converge.
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  3. #3
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    Re: Improper integrals

    Quote Originally Posted by kashmoneyrecord3 View Post
    Hey guys I'm having a little trouble with improper integrals in general and I came here looking for some help. I need to know which integrals are convergent and divergent and which integrals are improper.

    Can someone give me a couple points and tips when dealing with improper integrals.

    An example problem is x^4 e^-x^4 dx l infinity and 1
    Find a textbook with lots of examples. Your institute's library will have shelves of relevant books. Use a search like Google. Ask your teacher. etc.
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