# Fungrim entry: c285c7

Symbol: Integral $\int_{a}^{b} f(x) \, dx$ Integral
Integral(f(x), For(x, a, b)), rendered as $\int_{a}^{b} f(x) \, dx$, represents the integral of $f(x)$ from $a$ to $b$. The order is significant: $\int_{a}^{b} f(x) \, dx = -\int_{b}^{a} f(x) \, dx$.
Integral(f(x), ForElement(x, S)), rendered as $\int_{x \in S} f(x) \, dx$, represents the integral of $f(x)$ over the set $S$.
The special expression For(x, a, b) or ForElement(x, S) defines a locally bound variable.
The precise class of integrals allowed by this operator is yet to be defined, but should normally encompass Lebesgue integrals.
The integrand is allowed to be undefined on a subset of measure of zero.
Definitions:
Fungrim symbol Notation Short description
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Source code for this entry:
Entry(ID("c285c7"),
SymbolDefinition(Integral, Integral(f(x), For(x, a, b)), "Integral"),
Description(SourceForm(Integral(f(x), For(x, a, b))), ", rendered as ", Integral(f(x), For(x, a, b)), ", represents the integral of", f(x), "from", a, "to", b, ". ", "The order is significant: ", Equal(Integral(f(x), For(x, a, b)), Neg(Integral(f(x), For(x, b, a)))), "."),
Description(SourceForm(Integral(f(x), ForElement(x, S))), ", rendered as ", Integral(f(x), ForElement(x, S)), ", represents the integral of", f(x), "over the set", S, "."),
Description("The special expression", SourceForm(For(x, a, b)), "or", SourceForm(ForElement(x, S)), "defines a locally bound variable."),
Description("The precise class of integrals allowed by this operator is yet to be defined, but should normally encompass Lebesgue integrals."),
Description("The integrand is allowed to be undefined on a subset of measure of zero."))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC