With this unit, we move from derivatives to integrals. We approach these in two different ways: first, we look at what it means to take the inverse of a derivative, and then we try to look at the question of the area under a graph.
- Section 4.9: This section builds on the material from the Mean Value Theorem in order to find out how to reverse the process of differentiating. The results are called antiderivatives, or indefinite integrals.
- Section 5.1: In a section that initially seems unrelated to the previous one, we begin to explore the third great question behind the formation of calculus - what is the area defined by the graph of a function? We begin by examining how to get close to the answer, while the next section gets us to the value of the area itself.
- Section 5.2: Setting up the most important fact in calculus, which we will cover next week, this section takes the area estimates we had in Section 5.1 and makes them precise by taking their limits. The arithmetic is not trivial, but our ability to come up with answers should be seen as pretty impressive.