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Macaulay2Doc :: integrate

integrate -- numerical integration

Synopsis

Usage:

integrate(f, a, b)
Inputs:
- f, a function,
- a, a number, an infinite number, or an instance of the type Constant,
- b, a number, an infinite number, or an instance of the type Constant,
Outputs:
- a real number,

Description

Integrate f from a to b numerically, using Gaussian quadrature.

i1 : integrate(sin, 0, pi)

o1 = 2

o1 : RR (of precision 53)

For half-infinite intervals, 20-point Gauss-Laguerre quadrature is used.

i2 : integrate(x -> exp(-x), 0, infinity)

o2 = 1

o2 : RR (of precision 53)

For infinite intervals, 20-point Gauss-Hermite quadrature is used.

i3 : integrate(x -> exp(-x^2), -infinity, infinity)

o3 = 1.77245385090552

o3 : RR (of precision 53)

Ways to use `integrate` :

"integrate(Function,Constant,Constant)"
"integrate(Function,Constant,InfiniteNumber)"
"integrate(Function,Constant,Number)"
"integrate(Function,InfiniteNumber,Constant)"
"integrate(Function,InfiniteNumber,InfiniteNumber)"
"integrate(Function,InfiniteNumber,Number)"
"integrate(Function,Number,Constant)"
"integrate(Function,Number,InfiniteNumber)"
"integrate(Function,Number,Number)"

For the programmer

The object integrate is a method function.