The Definite Integral
Description:
In this unit, scholars will be introduced simultaneously to the concepts of area under a curve, integrals, and antiderivatives. The unit begins with the concrete applications of Riemann Sums to find the area under curves. It then introduces the notation of integrals to represent this area and the idea of positive vs. negative integrals. Scholars then learn the applications of integral notation through properties of definite integrals. The second half of the unit is dedicated to the idea of antiderivatives and their applications through the Fundamental Theorems of Calculus and average value. The unit ends with applications of integrals as seen on the AP examination, in particular the free-response sections.
Unit Essential Question:
"How does the concept of area under a curve connect to the other characteristics of functions?"