Calculus - Evaluating a definite integral by reversing the variable

[@mrrajiv82]

Just loved the way you teaches Hats Off!!

[@AvoidsPikes-]

I'm guessing that this method of evaluation is only used when the bounds of the integral are from 0 to 4? I'm thinking that we may have skipped this lesson (or I just don't remember it from Calculus.) Thank you MySecretMathTutor for these lessons that stimulate thinking (or bring on some math PTSD 😁)

[@MySecretMathTutor]

This is a fun "trick" to try out if your bounds go from 0 to some number. I don't think they show this in many calculus classes, so for many it will look brand new. I came across this technique when teaching a calculus course, and then once again when reading a book on integration techniques. It was so unique I just had to make a video. Thanks for those kind words. Keep up the good work! :^D

[@reaper4812]

I don't have a god damn clue how I am to know to use pi - x as my U in the second example.

[@MySecretMathTutor]

This is the key to "reversing the variable." Look at the bounds of this integral and think of the variable as changing from 0 to pi. If we wanted the variable to change from pi to 0 then the substitution u = pi - x (where x is the old variable) will get the job done. :^D