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WZ
Numerade Educator

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Problem 79 Hard Difficulty

Find the value of the constant $ C $ for which the integral
$$ \displaystyle \int_0^\infty \left (\frac{1}{\sqrt{x^2 + 4}} - \frac{C}{x + 2} \right)\ dx $$
converges. Evaluate the integral for this value of $ C $.

Answer

If $C<1, L=\infty$ and $I$ diverges.
If $C=1, L=2$ and $I$ converges to $\ln 2+\ln 2^{\circ}=\ln 2$
If $C>1, L=0$ and $I$ diverges to $-\infty$

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Video Transcript

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