Math 125 – Week 2

Reading Text – 5.3, 5.4 and 5.5
Worksheet Website – Relating antidifferentiation
to area under a curve
Fundamental.pdf
Worksheet 2 Solutions
Homework WebAssign WebAssign site for UW

### Student Guide:

The Fundamental Theorem of Calculus is stated in Section 5.3 and a sketch of the proof is given. There are two parts to the theorem and 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 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 covered here.

A lot of Math 125 is devoted to techniques for computing integrals. The technique of Substitution in presented in Section 5.5. You should understand its relation to the Chain Rule. There are two methods for solving a Definite Integral using Substitution.

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.