What is the integral of 0? - Mathematics Stack Exchange
Feb 4, 2018 · The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that the derivative of the function is the function's slope, because any function f …
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 …
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 …
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 …
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 …
LIATE : How does it work? - Mathematics Stack Exchange
Logs and inverse trig functions, when part of a more complicated integral, tend to cause problems. By differentiating them, you get 'simpler' more algebraic expressions, because $$\frac {d} {dx}\ln x=\frac …
Origin of the Integral (Theory Behind It - How it came about)?
Jul 1, 2015 · 3 How exactly was the integral derived? Like similarly to how the difference quotient explains where the derivative came from, what can we use to explain the origins of the integral? Like …
real analysis - Understanding Lebesgue Integral and Riemann Integral ...
May 3, 2025 · I'm reading Sheldon Axler's MIRA book and have trouble understanding the relationship between Lebesgue integral and Riemann integral. Here is the problem I want to solve: Let …
An integral that Wolfram Alpha can compute, but I want to know the ...
Jan 13, 2026 · The integral is $$\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 …
What is an Integral Domain? - Mathematics Stack Exchange
5 An integral domain is a ring with no zero divisors, i.e. $\rm\ xy = 0\ \Rightarrow\ x=0\ \ or\ \ y=0\:.\:$ Additionally it is a widespread convention to disallow as a domain the trivial one-element ring (or, …