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Math Help - improper integral

  1. #1
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    improper integral



    so:



    I know you're supposed to take the limit of the integrals, but I'm having trouble getting started.
    Without the limits, I found the indefinite integral to be 12arctan(sqrt(x)) +C
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  2. #2
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    well it converges, but you don't need to split it into two integrals, just put x=t^2.
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    well it converges, but you don't need to split it into two integrals, just put x=t^2.
    I'm still confused. how would that work?
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  4. #4
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    the substitution? just apply it, can you show what do you get?
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  5. #5
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    just subbing it in would just give \int\frac{6}{t(1+t^2)} would it not?
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  6. #6
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    no it's wrong, try again, the integrand has de arctangent form.
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  7. #7
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    so the integral would be 12arctan(t)+C which is equal to 12arctan(\sqrt(x))+C right?

    but after finding the integral, what do you do next to find the definite value from 0 to infinity?
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