What	Where	Link
Reading	Text – 4.9, 5.1 and 5.2
Worksheet	Website – The Area Problem	AreaProblem.pdf
Homework	Website	week1probs.pdf Selected Answers

Student Guide:

The course starts with antiderivatives. Given a function, you have to figure out what it is the derivative of. This usually involves some guess work. The term "Indefinite Integral" is just another name for an antiderivative. It is strongly recommended that you review your derivatives during the first week of the quarter.

Section 5.1 introduces the area problem and Riemann Sums (although this term isn't introduced until section 5.2). You should note that you have some freedom in choosing the sample points. Note especially that using the midpoint gives a good approximation.

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. Many properties of integrals are given using area-based geometric arguments.

• In integral calculus, we study functions that are defined as the area under some other function. The key idea is breaking a region up into slices, approximating the area of each slice with a rectangle, and then adding the areas of the rectangles up to get an estimate of the area of the region. With this in mind, AreaProblem.pdf will explore the idea of an area function. It will also guide you through the computation of the area under the graph of y = 1/x.
• The homework problems week1probs.pdf give a more examples of computing areas. The first three problems consist of selections from the textbook.
• Problem 4 focuses on approximating area. The methods of approximation used here can be considered an introduction to integration – when computing integrals to find areas (and later, to find lengths of curves), you are using concepts built off of approximations like the ones you make here.
• Problem 5 is more conceptual. You are asked to determine the units of a definite integral. This problem tests whether you understand what a definite integral means in a "real-world" context. (Later on, when you learn applications of integration, checking units in this manner can also give you a quick way of determining whether you are computing the correct integral.)