8.31.1 Top new questions this week

8.31.1.1 How to calculate this integral with highly oscillating integrand?
8.31.1.2 Explicit length of ticks in a Plot
8.31.1.3 How do I unlock a Mathematica Notebook?
8.31.1.4 Using CityData[] vs. Entity for population
8.31.1.5 Obtaining formula of $E[X^T A X B X^T CX]$ for Gaussian $X$
8.31.1.6 RegionIntersection for CountryData polygons
8.31.1.7 Replacement question
8.31.1.1 How to calculate this integral with highly oscillating integrand?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=273992

I mean 
$$\int_ 0^{2\pi}\frac {\sin (10050 t)\sin (10251 t)\cos (2022 t)} 
{\sin (50 t)\sin (51 t)} dt.$$ 
Here is my unsuccessful trial: 
... 
[calculus-and-analysis]
 
asked by user64494 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7152 Score of 10
answered by Goofy https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=46569 Score of 4
8.31.1.2 Explicit length of ticks in a Plot

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=273974

Ticks or Frameticks are defined in the following way: 
 {{x1,label1,len1},...}  tick marks with specified scaled length 
 
With the following information: 
... 
[plotting] [ticks]
 
asked by mathematica_guy https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=86803 Score of 8
answered by Daniel Huber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=46318 Score of 1
8.31.1.3 How do I unlock a Mathematica Notebook?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=274052

I downloaded Wolfram's Intro to Mathematica in Notebook format. I like to experiment as I study but you can't edit the notebooks. They are locked for some reason. So I still have to open a work ... 
[notebooks]
 
asked by cybervigilante https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=48241 Score of 7
answered by swish https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2490 Score of 14
8.31.1.4 Using CityData[] vs. Entity for population

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=274042

I am using v12.2.0-Win7-x64. 
 CityData[Entity[ 
"City", {"Shanghai", "Shanghai", "China"}], "Population"] 
 
 
... 
[curated-data] [geographics] [entity]
 
asked by Syed https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=81355 Score of 7
answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 Score of 5
8.31.1.5 Obtaining formula of $E[X^T A X B X^T CX]$ for Gaussian $X$

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=273893

Suppose $X$ is an $m\times n$ random matrix where rows are I.I.D. samples $x$ of $n$-dimensional Gaussian. The code at the end of the post verifies a candidate (incorrect) formula for the following ... 
[probability-or-statistics] [algebraic-manipulation]
 
asked by Yaroslav Bulatov https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=217 Score of 6
answered by user293787 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=85954 Score of 6
8.31.1.6 RegionIntersection for CountryData polygons

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=273943

I am using v12.2.0-Win7-x64. 
... 
[regions] [geography]
 
asked by Syed https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=81355 Score of 6
answered by kirma https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=3056 Score of 6
8.31.1.7 Replacement question

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=274036

I have this equation 
  F2 + F4 - V1 + V3==0 
 
I want it to be converted automatically  via a replacement rule to 
... 
[replacement]
 
asked by qahtah https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=46201 Score of 5
answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 Score of 7