Feb 17, 2025 · So an improper integral is a limit which is a number. Does it make sense to talk about a number being convergent/divergent? It's fixed and does not change with respect to the independent …

The integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $\int x^2 \mathrm {d}x$ in elementary functions …

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.

Definite integrals of that function are found by numerical methods rather than by finding a closed-form antiderivative. In exercises of this kind usually one gets the value of the integral either from software …

Dec 15, 2017 · A different type of integral, if you want to call it an integral, is a "path integral". These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to …

Oct 11, 2025 · However, one "intrinsic integral closure" that is often used is the normalization, which in the case on an integral domain is the integral closure in its field of fractions. It's the maximal integral …

@user599310, I am going to attempt some pseudo math to show it: $$ I^2 = \int e^-x^2 dx \times \int e^-x^2 dx = Area \times Area = Area^2$$ We can replace one x, with a dummy variable, move the …

5 An integral domain is a ring with no zero divisors, i.e. xy = 0 ⇒ x = 0 or y = 0. x y = 0 ⇒ x = 0 o r y = 0 Additionally it is a widespread convention to disallow as a domain the trivial one-element ring (or, …

Aug 20, 2023 · it works out because the integral is absolutely convergent (for x going to infinity the absolute value of the integrand behaves like x^2/x^4=1/x^2 which is integrable-look up cauchy …

Feb 5, 2020 · An integral transform "maps" an equation from its original "domain" into another domain. Manipulating and solving the equation in the target domain can be much easier than manipulation …