I'm looking for a fun (not too many tedious calculations) calculus one problem that uses the concept that, after subsitution, you have two integrals of diffent functions with different limits, but equal area. For example:
Those two regions are the same. I'm thinking of a problem that asks the student to prove two regions are of equal area, and once they set up the integrals they can see it is a case of subsitution.
Do you know of such a problem?