# Numerical integration over given integral. How to do it in Julia?

**URL:** <https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267>\
**Category:** New to Julia\
**Created:** [August 29, 2018, 8:30pm UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267 "2018-08-29T20:30:51Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![KZiemian](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kziemian/32/9020_2.png) [@KZiemian](https://discourse.julialang.org/u/KZiemian)\
**Post date:** [August 29, 2018, 8:30pm UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267/1 "2018-08-29T20:30:51Z")

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In my current work I integrate numericaly some function over [0, \infty) using NumPy calling of Fortran libraries. I want to try do my problem using Julia, but I can’t find out-of-the-box library computing integrals.

Can someone tell my how numerical integration look now in Julia? Do I need call Fortran code directly? I try google something, but find almost nothing.

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**Author:** ![HCrepaz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hcrepaz/32/4531_2.png) [@HCrepaz](https://discourse.julialang.org/u/HCrepaz)\
**Post date:** [August 29, 2018, 8:48pm UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267/2 "2018-08-29T20:48:42Z")

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Hi, There are several packages for numerical integration in Julia.

- For one-dimensional numerical integration **QuadGK.jl** [https://github.com/JuliaMath/QuadGK.jl](https://github.com/JuliaMath/QuadGK.jl)
- For higher dimensional quadrature **HCubature.jl** [https://github.com/stevengj/HCubature.jl](https://github.com/stevengj/HCubature.jl) or **NIntegration.jl** [https://github.com/pabloferz/NIntegration.jl](https://github.com/pabloferz/NIntegration.jl)

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [August 29, 2018, 11:10pm UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267/3 "2018-08-29T23:10:03Z")

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More explicitly, do `using Pkg; Pkg.add("QuadGK")` to install the QuadGK package, and then do

```julia
using QuadGK
quadgk(f, 0, Inf, rtol=1e-3)

```

to compute \int\_0^\infty f(x)dx (along with an error estimate) for a function `f`, to about 3–4 digits.

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**Author:** ![CarloLucibello](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/carlolucibello/32/3278_2.png) [@CarloLucibello](https://discourse.julialang.org/u/CarloLucibello)\
**Post date:** [August 30, 2018, 7:51am UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267/4 "2018-08-30T07:51:08Z")

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Does anyone know how to perfom numerical integration on a gpu?

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [August 30, 2018, 8:03am UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267/5 "2018-08-30T08:03:24Z")

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> [@CarloLucibello](#):
>
> Does anyone know how to perfom numerical integration on a gpu?

Use [GitHub - JuliaApproximation/FastGaussQuadrature.jl: Julia package for Gaussian quadrature](https://github.com/ajt60gaibb/FastGaussQuadrature.jl) to get the quadrature rates, use a CUArray and broadcast your function across the array, and then accumulate according to the quadrature weights.

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**Author:** ![CarloLucibello](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/carlolucibello/32/3278_2.png) [@CarloLucibello](https://discourse.julialang.org/u/CarloLucibello)\
**Post date:** [August 30, 2018, 8:11am UTC](https://discourse.julialang.org/t/numerical-integration-over-given-integral-how-to-do-it-in-julia/14267/6 "2018-08-30T08:11:28Z")

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this would work, thanks!