Converting an Improper Integral
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Let f be a non-negative monotone continuous function defined on the interval (0 <). Suppose that the improper integral f(x)dx integrated is convergent. Prove that f is bounded on (0<) and the limit as x goes to infinity of f(x) is 0.
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Solution Summary
This solution explains how to prove that f is bounded on (0<) and the limit as x goes to infinity of f(x) is 0.
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Proof:
Case 1: f(x) = 0 for all x between 0 and infinity. This is a trivial case. We must have the limit as x ...
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