# Estimating function intergral - function containing a sine or a cosine

**URL:** <https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139>\
**Category:** General Usage\
**Created:** [March 18, 2020, 1:00pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139 "2020-03-18T13:00:48Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![timmm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/timmm/32/6760_2.png) [@timmm](https://discourse.julialang.org/u/timmm)\
**Post date:** [March 18, 2020, 1:00pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139/1 "2020-03-18T13:00:48Z")

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Hi Julia users,

I am looking for a package with functionality similar to the FORTRAN package QDAWO: [https://docs.roguewave.com/en/imsl/fortran/2018.0/html/fnlmath/index.html#page/FNLMath/mch4.07.08.html](https://docs.roguewave.com/en/imsl/fortran/2018.0/html/fnlmath/index.html#page/FNLMath/mch4.07.08.html).

The FORTRAN function

Takes:

- function F that evaluates X
- a simple weight function cos(omega \* x) or sin(omega \* x)
- integration limits
- some optional accuracy args

Returns:

- Estimate of the integral from A to B of F \* weight. (Output)

Does anyone have any suggestions?  
Cheers,  
Tim

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<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [March 18, 2020, 1:02pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139/2 "2020-03-18T13:02:12Z")

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I think QuadGK.jl is a good option for this, if I understand the problem correctly.

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<div class="post-metadata">

**Author:** ![timmm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/timmm/32/6760_2.png) [@timmm](https://discourse.julialang.org/u/timmm)\
**Post date:** [March 18, 2020, 1:44pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139/3 "2020-03-18T13:44:11Z")

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Great, do you have an example of how to integrate the example given for the FORTRAN package with QuadGK? (see the bottom of the page in the link)  
 ![Func](https://global.discourse-cdn.com/julialang/original/3X/d/6/d623725a0310520335555e70597a805430e9f705.png)  
where sin(10 pi x) is the weight function.

Tim

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<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [March 18, 2020, 2:48pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139/4 "2020-03-18T14:48:17Z")

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```julia
julia> using QuadGK

julia> I, err = quadgk(x -> log(x) * sin(10π * x), 0, 1)
(-0.12813684841011241, 6.022027749476766e-10)

```

`err` is an estimate of the error.

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<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [March 18, 2020, 2:58pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139/5 "2020-03-18T14:58:19Z")

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If you need more precision:

```julia
julia> quadgk(x -> log(x) * sinpi(10 * x), big(0), big(1))
(-0.1281368483991673319461205998814827821390661153292255454760992739874546286851618, 5.320715261059094679776530339302038795574511819139725448727858206949982301331101e-40)

```

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<div class="post-metadata">

**Author:** ![timmm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/timmm/32/6760_2.png) [@timmm](https://discourse.julialang.org/u/timmm)\
**Post date:** [March 18, 2020, 3:01pm UTC](https://discourse.julialang.org/t/estimating-function-intergral-function-containing-a-sine-or-a-cosine/36139/6 "2020-03-18T15:01:32Z")

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Great, that’s really simple.

Cheers,  
Tim