This result, while taught early in elementary calculus courses, is actually a very deep result connecting the purely algebraic indefinite integral and the purely analytic (or geometric) definite integral.
Here are a set of practice problems for the Calculus I notes.
Review - In this chapter we give a brief review of selected topics from Algebra and Trig that are vital to surviving a Calculus course.
Included are Functions, Trig Functions, Solving Trig Equations and Equations, Exponential/Logarithm Functions and Solving Exponential/Logarithm Equations.
We will discuss the interpretation/meaning of a limit, how to evaluate limits, the definition and evaluation of one-sided limits, evaluation of infinite limits, evaluation of limits at infinity, continuity and the Intermediate Value Theorem.
We will also give a brief introduction to a precise definition of the limit and how to use it to evaluate limits Tangent Lines and Rates of Change – In this section we will introduce two problems that we will see time and again in this course : Rate of Change of a function and Tangent Lines to functions.
We will cover the basic notation, relationship between the trig functions, the right triangle definition of the trig functions.
We will also cover evaluation of trig functions as well as the unit circle (one of the most important ideas from a trig class!
The only difference is that the answers in here can be a little messy due to the need of a calculator.
Included is a brief discussion of inverse trig functions.