MATH 208 Introduction Review

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Syllabus Let’s go over it in detail. Please pay attention. I will be giving you a short quiz next time about its contents!

A couple more things…

About you At the end of today’s session: turn in the “Who Am I” handout I gave you. Fill in as much as is comfortable for you on it. All info will be appreciated and will help to get to know you better. Let’s go around and mention our Name and Superpower 

Now let’s review a few things…

Several review links are posted on the class website! For example: PreCalculus Tutorials MATH2.org  Midnight Tutor Videos Just Math Tutorials All of my Math 207!

Integrals review

The Definite Integral  

Net Area on interval [-1,9]? Total Area on interval [-1,9]?

Fundamental Theorem of Calculus: Suppose that f is bounded on the interval [a,b], and that F is an antiderivative of f, i.e.,  F’ = f.     Then:

Fundamental Theorem of Calculus – simplest form: Fundamental Theorem of Calculus – more general form:

Example 1: Solution:

Example 2: Solution:

Example 3: Solution:

You can find more practice problems with solutions here: http://tutorial.math.lamar.edu/Classes/CalcI/ComputingDefiniteIntegrals.aspx

Substitution Rule

Examples: Evaluate the following: Indefinite integral:  x3 cos(x4 + 2) dx Definite integral:

Solutions: 1) We make the substitution u = x4 + 2 because its differential is du = 4x3 dx, which, apart from the constant factor 4, occurs in the integral. Thus, using x3 dx =(1/4)du and the Substitution Rule, we have  x3 cos(x4 + 2) dx = (1/4)  cos u  du = (1/4)  cos u du = (1/4) sin u + C = (1/4) sin(x4 + 2) + C

2) Let u = 2x + 1. Then du = 2 dx, so dx = (1/2) du. (complete this blank!) 4