solving the integral of $e^ {x^2}$ - Mathematics Stack Exchange
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 …
How to calculate the integral in normal distribution?
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 …
What does it mean for an "integral" to be convergent?
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 …
What is an integral? - Mathematics Stack Exchange
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 …
calculus - Is there really no way to integrate $e^ {-x^2 ...
@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 …
An integral that Wolfram Alpha can compute, but I want to know the ...
Jan 13, 2026 · The integral is $$\int_0^ {\infty}\frac {e^ {-\frac {1+4y^2} {4y}}} {\sqrt {4\pi y}}dy$$ which Wolfram Alpha computes to $\frac 1 {2e}$. I would like to know the steps. I noticed the integral is …
Can the integral closure of a ring be taken intrinsically?
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 …
integration - reference for multidimensional gaussian integral ...
I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are
calculus - How to deal with a substitution that makes both the limits ...
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 …
What is an Integral Domain? - Mathematics Stack Exchange
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, …