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

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

Operators