1. MATH 208
Introduction
Review

2. Brightspace: brightspace.ccc.edu
What is it?
It replaces Blackboard. Adios Blackboard!
How do I log in?
With my ccc credentials (login and password)
DO it now! (on your tablet/phone…)
Set up your profile to get my messages.
Look around the contents.

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

4. A couple more things…

5. 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 

6. Now let’s review a few things…

7. 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!

8. Integrals review

11. The Definite Integral

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

14. 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:

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

16. Example 1:
Solution:

17. Example 2:
Solution:

18. Example 3:
Solution:

19. You can find more practice problems with solutions here:

20. Substitution Rule

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

24. 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

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