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Recently I learned about "King's Property" or "King's Rule" and I was wondering about its etymology? I understand that it's a basic change of variables but it has a name for a reason. I've been unable to find this reason online. I speculate that the person who first encountered it had the popular surname King.

In case terminology is different elsewhere, here's what I'm talking about:$$\int_{a}^{b}f(x)dx=\int_{a}^{b}f(a+b-x)dx$$

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1 Answer

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I have never heard this referred to as "King's Property" or "King's Rule". And there is almost nothing (except this thread) in Google. There is this video, maybe your answer is there. (Video can be viewed only by paid students) Maybe the term "King's Property" is unique to that video.

The video is from an educational company (?) called Nucleon, located in Rajasthan, in northern India. "Rajasthan" means "Land of Kings".

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As pointed out in a comment, the "King's Property" has been mentioned in math.se before. The oldest one seems to be Trigonometric definite integration . That post is from July, 2017. The post is by Tarun Raj Latiyan. Wouldn't it be interesting if Tarun is from India and learned this terminology from the Nucleon video?

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