Calc 2, Lec 12B: NASTY-Looking Improper Integral! Does It Converge or Diverge? Prove Your Answer!
Does the improper integral from 1 to infinity of (sin(x)+4)/(x^2) converge or diverge? This looks hard enough that you wouldn't want to try to compute it by hand as a limit. But the Comparison Test for improper integrals helps us prove that it converges fairly easily. We just need the fact that sin(x) is bounded between -1 and 1 for all x.
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