Can you explain and solve an improper integral where the integrand has an infinite discontinuity and demonstrate its convergence using the comparison test?
Answer 1
Hannah Peters
Consider the improper integral ∫(1/x^2) dx from 1 to ∞. The integrand 1/x^2 has an infinite discontinuity at x = 0. To demonstrate convergence, compare it with ∫(1/x^2) dx from 1 to ∞, which converges because ∫(1/x^p) dx converges for p > 1. Hence, the original integral converges.
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