S2E24: Integral evaluation via Scope Reduction скачать в хорошем качестве

S2E24: Integral evaluation via Scope Reduction

In this episode we apply the Scope Reduction problem-solving approach to an evaluation of a definite Riemann integral by avoiding a direct or a traditional fight with such integral and by reducing the current, difficult to solve, problem to a previously solved problem. As such, we are done with this problem in the space of 2 minutes or less. However, as usual, it pays to both solve the "previously solved problem" and to understand where Mathematics in this experience begins and ends. The reason for solving the "previously solved problem" is pedagogical, because by solving the "previously solved problem" by-hand and ourselves we better comprehend the actual amount of work that the "previously solved problem" is saving us and by so doing we also begin to realize the power of the Scope Reduction problem-solving approach. As we partition our current experience into "Mathematics" and "not Mathematics" we, hopefully, see that "Mathematics" in this case was the process of generating the idea of introducing the helper function, please see 6:24, and everything else that followed was "not Mathematics".