1. Definite Integration Say good-bye to C
Section 4-2-a
Definite Integration
Say good-bye to C

2. 1st Fundamental Theorem of Calculus
If a function is continuous on the closed interval [a,b] and F is an antiderivative of f on the interval, then
The constant C is not necessary because

3. Notation for Definite Integrals
a and b are called the limits of integration. They are attached to the integral symbol. The lower limit a is usually a left side boundary and the upper limit b is usually a right side boundary. Integrating produces an answer called the definite integral value.

4. 2) Evaluate
3) Evaluate

5. 4) Evaluate
5) Evaluate

6. Properties of definite integrals
I) If is defined at x = a, then
II) If is integratable on [a,b], then
III) If is integratable on three closed intervals determined by a, b, and c, then

7. Properties continued
IV) If is an even function (recall f(x) = f(-x), all exponents are even, symmetric with the y- axis) then
V) If is an odd function (recall f(-x) = -f(x), all exponents are odd, symmetric with the origin) then

8. 6) Given
Find a) b) c) d)

9. 7) Evaluate

10. 8) Evaluate

11. 9) Evaluate

12. Homework Worksheet 4-2A and Page 278 # 33, 34, 35, 36, 38, 40,
41, 42 and 43 using the given values