Calculus - Evaluating a definite integral by reversing the variable

In this video we'll go over how you can evaluate some definite integrals by using a u-substitution that reverses the original variable. There are lots of twist and turns in this one so watch carefully. Remember you might have to combine your work with the original integral.
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This video is related to many other topics. Check them out:
The basics of indefinite integrals: • Calculus - The basics ...
U substitution for integrals: • Calculus - u substitut...
Derivative of sin and cos: • Calculus - Derivative ...
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[@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