Students write the two fundamental theorems of Calculus. (I call them First and Second Fundamental Theorem, but different textbooks teach them in different orders – same theorems!!!) Then the students work lots of examples with each – symbolically, graphically, abstractly, using a tabular function and in an application problem. Comparing them side by side reinforces that one of them is the integral of a derivative and the other is the derivative of an integral.
My students encounter this concept in the Larsen Calculus textbook in Ch. 4 on Integration after they learn simple antiderivatives, definite integrals Riemann and trapezoidal sums, and integration strategies thus the numbering 4-4. The examples do not involve the transcendental functions which are introduced in a later chapter in Larson Calculus.
This foldable is formatted so that it can be used alone or glued into an Interactive Notebook. Hope this is helpful. Enjoy!
Other foldables related to the Integration chapter:
Calculus Foldable 4-1: Simple Antiderivative Rules
Calculus Foldable 4-2: Integral as Area
Calculus Foldable 4-3: Integration Strategies
Calculus Foldable 4-5: Mean Value Theorems of Calculus
Table of Contents for the Integration chapter:
Calculus Interactive Notebook 4: Integration