Interpret and represent an infinite Riemann sum as a definite integral.
I can use limits to explain how a Riemann Sum approximation can be improved to find the exact area under a curve.
I can use definite integral notation to represent the exact area under a curve.
Quick Lesson Plan
In preparation for Quiz 6.1 – 6.3, today’s review activities focus on the skills and content of Topics 6.1 – 6.3: the concept of accumulation, approximations using Riemann sums and trapezoidal sums, and the development of the integral as a limit of approximating Riemann sums. We provided a wide variety of tasks for students: original “Open Middle” integral expressions to encourage exploration of different integrands; a “Four Corners” themed worksheet to practice the four required representations (graphical, verbal, analytical, numerical); an in-depth investigation of integrands reflecting transformations of f(x) = sin x and the limits of integration.
Complex expressions provide the basis for our work with the Fundamental Theorem, integration by parts, partial fractions, differential equations, and more. Correct notation communicates these complex ideas to the reader (the AP Reader as well!) and must be practiced and perfected by students.
Encourage student-to-student conversation and group work during these review activities as some students will benefit from the informal instruction of their peers! At the conclusion of your focused review activities, distribute FRQs from past AP Tests which reflect the learning objectives and skills from the relevant topics or allow time for students to complete previously assigned homework problems.