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What does it mean for an integral to be convergent? The improper integral $\int_a^\infty f(x) \, dx$ is called convergent if the corresponding limit exists and divergent if the limit does not exist While I can understand this intuitively, I have an issue with saying that the mathematical object we defined as improper integrals is "convergent" or "divergent"
How to calculate the integral in normal distribution? It goes without saying that if you're trying to find a CDF, you need to add limits and evaluate the definite integral In the second equation you'll notice that I used "a" as the (upper) limit variable And the question is talking about the CDF, so the lower limit is negative infinity $\endgroup$ –
integration - Improper integral of sin(x) x from zero to infinity . . . I was having trouble with the following integral: $\int_{0}^\infty \frac{\sin(x)}{x}dx$ My question is, how does one go about evaluating this, since its existence seems fairly intuitive, while its solution, at least to me, does not seem particularly obvious
Really advanced techniques of integration (definite or indefinite) The technique had the added advantage of being simple, requiring only slightly more effort to learn than the Riemann integral There was in fact a (failed) movement to replace the teaching of the Riemann integral with that of the Kurzweil-Henstock integral (also called generalized Riemann integral and gauge integral)
What is the integral of 1 x? - Mathematics Stack Exchange $\begingroup$ "Answers to the question of the integral of 1x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers" --- not completely correct: if they are both negative it also works This is an improper integral and does not converge in the remaining cases $\endgroup$ –