What	Where	Link
Reading	Text – 5.3, 5.4 and 5.5
Worksheet	Website – Relating antidifferentiation to area under a curve	Fundamental.pdf
Homework	Website	week2probs.pdf Selected Answers

Student Guide:

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 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.

• 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 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..
• The first three homework problems in week2probs.pdf consist of selections from the textbook.
• Problems 4, 6 and 7 are typical applications of this material. Make sure you become comfortable doing this style of problem, you will see many others like these.
• It is important that you understand not just the statement of the Fundamental Theorem of Calculus, but also that you understand what it means with respect to the graph of a function. Problem 5 deals with this geometric meaning of the Theorem.
• Problem 8 is similar in concept to 5, but requires that you also understand the meaning of the integral with regard to physical quantities (c.f. last week's homework, Problem 5).