## Math 125: Week 1

 Math 125 main page Week 2 outline

Reading Text -- Sections 4.9, 5.1, 5.2
Worksheet    Website – The Area Problem AreaProblem.pdf
Worksheet 1 Solutions (available after Thursday)
Homework WebAssign WebAssign site for UW

### Student Guide:

The course starts with the notion of antiderivatives, in section 4.9: given a function f(x), we want find another function F(x), which differentiates to the original function f(x). 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 derivative formulas from Calc I 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 definite integrals are given using area-based geometric arguments.

WORKSHEET: In integral calculus, we study functions that are defined as the area under the graph of some other function. The key idea is to break a region up into slices, approximating the area of each slice with a rectangle, and then to add the areas of the rectangles to get an estimate of the area of the entire region. With this in mind, the worksheet 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.

 Math 125 main page Week 2 outline