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 …

@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 …

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 …

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 …

May 3, 2025 · I'm reading Sheldon Axler's MIRA book and have trouble understanding the relationship between Lebesgue integral and Riemann integral. Here is the problem I want to solve: Let …

Mar 10, 2023 · I think that makes sense to me. But, what is the conceptual idea behind arc length (total distance) being the integral of the speed? What exactly are you adding up? Tiny slices of speed …

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, …