Evaluate the improper integral .
Answer and explanation
Correct answer: C.
- Step 1: Evaluate the limit of proper integrals: . \lim_{b o +\infty} \left( -\frac{1}{b} - (-1) ight) = 0 + 1 = 1. The improper integral converges to . **Answer: . Why not the others:** " divergent sum" confuses the convergent -series integral () with the divergent harmonic integral (); " vanishing tail" evaluates only the asymptotic limit while dropping the lower limit contribution ; " quadratic area" incorrectly integrates as .
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