Math 125: Week 2
| Week 1 outline | Math 125 main page | Week 3 outline |
| What | Where | Link |
|---|---|---|
| Reading | Text -- 5.2, 5.3, 5.4 | |
| Worksheet | Website – Relating antidifferentiation to area under a curve | Fundamental.pdf Worksheet 2 Solutions (available after Thursday) |
Student Guide:
The definition of the Definite Integral as a limit of Riemann Sums is given in section 5.2. The concept of "area" vs. "signed area" is introduced, and many properties of integrals are given, using area-based geometric arguments.
The Fundamental Theorem of Calculus is stated in Section 5.3, and a sketch of its proof is given. There are two parts to the theorem -- you need to understand both! Make sure you understand the hypotheses of the theorem: see Example 9 in the text. Some functions that are defined as integrals with variable bounds are presented in this section.
Indefinite Integrals are introduced in Section 5.4. You should understand how they differ from Definite Integrals. You should see graphically how the solution to an Indefinite Integral is a whole family of functions. The difference between Net Change and Total Change is also covered here.
WORKSHEET: Given a function f(x), we can define the area function A(x) which computes the area under f(x). The Fundamental Theorem of Calculus gives a nice relationship between f(x) and A(x). This relationship is explored in the worksheet Fundamental.pdf with an emphasis on graphical thinking. This worksheet also shows you how to apply integral calculus to distance and velocity problems and considers net and total change.
| Week 1 outline | Math 125 main page | Week 3 outline |