Q: Does ∫₁^∞(1/x²)dx converge? What about ∫₀¹(1/√x)dx? ∫₁ᵇ1/x² = 1-1/b → 1: CONVERGES to 1! ∫₀¹1/√x: ∫ₐ¹x^(-1/2) = 2-2√a → 2: CONVERGES (singularity tamed!)! ∫₁^∞1/x = ln b → ∞: DIVERGES!