Chapter 7: Q. 1TB (page 630)
The comparison test: In Section 5.6 we discussed the comparison test for improper integrals.
- What is the comparison test for improper integrals?
- How is the comparison test for improper integrals used to analyze the convergence or divergence of an improper integral?
- Which improper integrals are used in the comparison test?
Short Answer
If \int_a^{\infty} f(x) d x converges, then \int_a^{\infty} g(x) d x converges.
If \int_a^{\infty} g(x) d x diverges, then \int_a^{\infty} f(x) d x diverges.
The limit comparison test and comparison test are used in the comparison test.