Web Reference: Feb 28, 2026 · I have an integral, $$ I = \int_a^b x f (x) dx $$ and I would like to express this in terms of $\int_a^b f (x) dx$ if possible, but I don't see how integration by parts will help here. Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers. Feb 17, 2025 · The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined. If the appropriate limit exists, we attach the property "convergent" to that expression and use the same expression for the limit.
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