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Math Help - Evaluating improper integral for constant (C)

  1. #1
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    Evaluating improper integral for constant (C)

    Find the value of the constant C for which the integral \int_{0}^{\infty}(\frac{1}{\sqrt{x^{2} + 4}} -\frac{C}{x + 2})dx converges. Evaluate the integral for this value of C.

    I dont understand how you can find a constant C for convergence, I thought that the only way to test for convergence, is by actually evaluating the integral or using the comparison test.
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  2. #2
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    Carry out the integration as it stands, (you get two logs which can then be combined), and then ask yourself what value C must take in order that the integrand is not infinite at the top limit.
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