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Math Help - comparison test for improper integrals

  1. #1
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    comparison test for improper integrals

    I have to use the comparison test to determine if the integral diverges or converges but I am confused about how to do this. Please help.

    integral from 1 to infinity of dx/(square root(x^4 + 4x^3))
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  2. #2
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    This was posted before, anyway, for x\ge1 it's \frac{1}{\sqrt{{{x}^{4}}+4{{x}^{3}}}}\le \frac{1}{\sqrt{{{x}^{4}}}}=\frac{1}{{{x}^{2}}}, so your integral converges by direct comparison with \int_1^\infty\frac{dx}{x^2}.
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  3. #3
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    okay so if the bounds change to from 0 to 1 it would be divergent?
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  4. #4
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