# Integration of |∇p|^2
**URL:** https://discourse.julialang.org/t/integration-of-p-2/116671
**Category:** Optimization (Mathematical)
**Created:** [July 5, 2024, 4:49pm UTC](https://discourse.julialang.org/t/integration-of-p-2/116671 "2024-07-05T16:49:29Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Banan\_alkafri](https://discourse.julialang.org/u/Banan_alkafri)
#### Post date: [July 5, 2024, 4:49pm UTC](https://discourse.julialang.org/t/integration-of-p-2/116671/1 "2024-07-05T16:49:29Z")
I want to create a function that integrates the magnitude of the gradient of a polynomial with 2 variables squared. I created a generic polynomial using monomials and calculated |∇p|^2 and now i have a polynomial that consists of two variables and some of the terms have a combination of the two variables. I want to integrate w.r.t x first and then y. I know the general formula of integrating a polynomial but I’m integrating w.r.t one variable only then how can I work it out? I’m don’t want to use any package that will integrate it directly.
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### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 5, 2024, 7:51pm UTC](https://discourse.julialang.org/t/integration-of-p-2/116671/2 "2024-07-05T19:51:05Z")
Perhaps Polynomials.jl has part of the solution?
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### Author:  [@nsajko](https://discourse.julialang.org/u/nsajko)
#### Post date: [July 5, 2024, 8:03pm UTC](https://discourse.julialang.org/t/integration-of-p-2/116671/3 "2024-07-05T20:03:47Z")
> [@Banan\_alkafri](#):
>
> I know the general formula of integrating a polynomial but I’m integrating w.r.t one variable only then how can I work it out?
I think you simply want to treat the other variable as a constant.
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### Author:  [@Banan\_alkafri](https://discourse.julialang.org/u/Banan_alkafri)
#### Post date: [July 5, 2024, 9:20pm UTC](https://discourse.julialang.org/t/integration-of-p-2/116671/4 "2024-07-05T21:20:47Z")
yes, this is what I want to do.