# Function defined as multidimensional integral

**URL:** <https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535>\
**Category:** New to Julia\
**Tags:** question, integral\
**Created:** [December 23, 2021, 4:13pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535 "2021-12-23T16:13:30Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Federico\_Compagnin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/federico_compagnin/32/32170_2.png) [@Federico\_Compagnin](https://discourse.julialang.org/u/Federico_Compagnin)\
**Post date:** [December 23, 2021, 4:13pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535/1 "2021-12-23T16:13:30Z")

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Hi, I’m trying to define a new function as follows:

![Screenshot 2021-12-23 at 17.11.46](https://global.discourse-cdn.com/julialang/original/3X/8/0/8064948a27d477079cc8d14bc0a029021f995235.png)

meaning, I’d like to integrate over x and y, leaving z as a variable. I thought maybe to integrate z over (0,z) and then differentiate the function with respect to z, but it seems to me quite intricate. Any ideas?

Thanks a lot

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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:** [December 23, 2021, 4:26pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535/2 "2021-12-23T16:26:29Z")

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h(z) = hcubature((x,y)-\>f(x,y,z),…). It’s called a closure.

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**Author:** ![Federico\_Compagnin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/federico_compagnin/32/32170_2.png) [@Federico\_Compagnin](https://discourse.julialang.org/u/Federico_Compagnin)\
**Post date:** [December 23, 2021, 4:46pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535/3 "2021-12-23T16:46:43Z")

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That’s interesting! I’m still learning Julia, so this is something new for me.  
Trying to implement this closure, I got the following method matching error: how can it be? Those #9#10 aren’t so clear to me

 ![Screenshot 2021-12-23 at 17.45.09](https://global.discourse-cdn.com/julialang/original/3X/e/3/e3eae98c0c02cfffd7c9275c208cfc3362c4c8be.png)

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<div class="post-metadata">

**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:** [December 23, 2021, 5:00pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535/4 "2021-12-23T17:00:42Z")

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Oh it’s giving you an SVector instead of two arguments, so it’s x[1] etc. You can write that all out, or use the simpler syntax h(z) = hcubature((x)-\>f(x…,z),…) to splat it

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<div class="post-metadata">

**Author:** ![Federico\_Compagnin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/federico_compagnin/32/32170_2.png) [@Federico\_Compagnin](https://discourse.julialang.org/u/Federico_Compagnin)\
**Post date:** [December 23, 2021, 5:09pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535/5 "2021-12-23T17:09:15Z")

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I love this syntax!  
Thank you a lot

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**Author:** ![gustaphe](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gustaphe/32/18174_2.png) [@gustaphe](https://discourse.julialang.org/u/gustaphe)\
**Post date:** [December 23, 2021, 6:31pm UTC](https://discourse.julialang.org/t/function-defined-as-multidimensional-integral/73535/6 "2021-12-23T18:31:26Z")

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Welcome! For the future: please share code as text instead of images. Makes it easier to read, copy and run. You can use a triple backtick fence to get monospace font and syntax highlighting.

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