A Peculiar Property of Definite Integrals // The King Rule (The Art of Integration)

In this video we introduce a peculiar property of definite integrals that's known in some places as the King Rule.
On our journey to evaluate difficult integrals we've needed to expand our mathematical toolbox to be able to increase our creative problem solving skills. We've used algebraic tricks, creative substitutions, and advanced results like Euler's formula and the gamma function. We're now ready to introduce a simple property of definite integrals that's incredibly useful for a large class of integrals. At first glance this property doesn't seem to be of much use. However, we'll see just how useful it is after going through two good introductory problems. Timestamps for the different parts are below:
0:00 Introduction
1:49 Geometric Meaning
5:51 Proof
10:43 Alternate Version
13:19 Problem 1
16:59 Problem 2
The Art of Integration is an ongoing series where we evaluate integrals with techniques that are not typically taught in the calculus sequence. This is a great way for students in science, engineering, and mathematics to strengthen their integration skills and creativity in solving problems. Most of the problems should be accessible to students that have covered the integration methods from calculus 2.
Looking for a specific problem or topic? Try checking my website:
www.blacktshirtmathprofessor....
► Artist Attribution
Music By: "After The Fall"
Track Name: "Pieces"
Music Published by: Chill Out Records LLC
License: Creative Commons Attribution 4.0 International (CC BY - 4.0)
Full license here: creativecommons.org/licenses​

[@philiplee3925]

This is underrated

[@BlackTshirtMathProfessor]

It’s one of my favorite techniques to try on difficult integrals

[@mattikemppinen6750]

Very clear and concise explanation, thanks! Just learned about this property, it's a great addition to anyone's bag of integration tricks =)

[@johanndohmann1281]

Great Video.Thanks a lot. Your "trig" identities are "tricky" identities as well. Best wishes from germany

[@mihaipuiu6231]

Your writing is very nice and your explanation is the same. I'd prefer all the teachers to be like you. Thanks.

[@leleep_]

Somebody count the number of times he pointed at us

[@BlackTshirtMathProfessor]

Not enough times. I’ll re-record this video and include more pointing.

[@manojsurya1005]

The geometric proof for it was lit! And the problems were good too😄

[@BlackTshirtMathProfessor]

Yeah, the geometric proof is pretty cool!

[@PrateekShukla400]

Nicely explained sir! Appreciate that.

[@BlackTshirtMathProfessor]

Glad you enjoyed it, fellow mathematician!

[@recipehill]

numste sir ji

[@divyanshudubeyrdx5370]

Hello sir, sorry sir I am not able to view your videos because I was preparing for exam.... sorry....
Well explained video sir pls give its 2nd part part

[@BlackTshirtMathProfessor]

More are on the way. A lot of the standard integrals where the King Rule can be used involve trig functions so I’m taking some time to make up some integrals without them.

[@divyanshudubeyrdx5370]

@@BlackTshirtMathProfessor ok sir best of luck

[@guljaralam3447]

Tanks sir

[@BlackTshirtMathProfessor]

You’re welcome! I’m glad you liked it.

[@guljaralam3447]

Question sir

[@guljaralam3447]

logsinx limit 90and0 me

[@guljaralam3447]

King rules

[@BlackTshirtMathProfessor]

I already did it. Check it out at this link:
Peculiar Property of Definite Integrals Problem 1 (The Art of Integration)
czcams.com/video/R6giSk0X3ow/video.html

[@uniquelearningexperiment5456]

Love ❤️ you sir 🙏🙏🙏🙏

[@BlackTshirtMathProfessor]

Thank you so much!