10.21.1 Top new questions this week

10.21.1.1 Numerical approximation of the integral by using data

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304518

I want to use the numerical approximation of the integral of a function given a list of data: 
$$\int_a^bf(x)dx\approx\sum_{k=1}^N\frac{f(x_{k})+f(x_{k-1})}{2}(x_{k}-x_{k-1}),$$ 
where $f(x_0)=f(a)$ and ... 
[calculus-and-analysis] [numerical-integration] [algorithm]
 

asked by Patrick El Pollo https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=26743 Score of 9

answered by zeraoulia rafik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=66737 Score of 5

10.21.1.2 How to make Region from Spline curve

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304499

Let 
 bsf = BSplineFunction[{{1, 1}, {-0.5, -0.7}, {-0.4, -1}, {1, 0}}, 
SplineClosed -> True, SplineDegree -> 3] 
 
 
Than 
... 
[regions] [parametric-functions] [splines]
 

asked by lesobrod https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5950 Score of 8

answered by cvgmt https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72111 Score of 13

10.21.1.3 Adding shadows to spiric sections of a torus

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304541

While adding shadows to the spiric sections of a torus using the The answer to the question given by Daniel Huber, I faced a problem. 
Instead of being well separated as previously, the sections ... 
[plotting] [graphics] [graphics3d] [map] [mapthread]
 

asked by user444 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=84456 Score of 6

answered by cvgmt https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72111 Score of 10

10.21.1.4 How can I permute pair of elements in a list?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304437

How can I find all permutations (ways of exchanging positions of pairs in brackets) in a list? The position of elements not in pair should not change. 
... 
[list-manipulation] [function-construction]
 

asked by internet https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=87122 Score of 6

answered by A. Kato https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=62063 Score of 5

10.21.1.5 Detecting and converting a number from a video (digital panel) into an actual number

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304604

Let's say I have video (mp4) of length 02:17:38 (hh:mm:ss), this video is a record of a temperature panel, as shown in the following image. How can I use mathematica to extract the temperature, given ... 
[image-processing] [scripting] [video]
 

asked by Hussain-Alqatari https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=73010 Score of 5

answered by ydd https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72953 Score of 2

10.21.1.6 Integration involving Piecewise function and DiracDelta function

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304515

I want to calculate an integration, which reads 
 
where $\delta\left(q_{23}^{01}\right)=\delta\left(1+q_1-q_2-q_3\right)$ and $\mathrm{min}(1,q_1,q_2,q_3)$ means the minimum of $(1,q_1,q_2,q_3)$. 
What ... 
[calculus-and-analysis] [special-functions] [integral-equations]
 

asked by so_sure https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=73637 Score of 5

answered by zeraoulia rafik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=66737 Score of 3

10.21.1.7 Voronoi mesh of a circular image

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=304593

I have a circular image (below) and would like to obtain a Voronoi mesh. 
 
I am able to obtain the centers of the cells inside the image as 
... 
[mesh]
 

asked by Rachele Allena https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=99595 Score of 5