1. Definite Integrals and Antiderivatives
5.3
Definite Integrals and Antiderivatives

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about
Properties of Definite Integrals
Average Value of a Function
Mean Value Theorem for Definite Integrals
Connecting Differential and Integral Calculus
Essential Questions
What are the properties of definite integrals and
how do they help us to understand how definite
integrals are connected to Integral Calculus?

5. Rules for Definite Integrals
Order of Integration:
Zero:
Constant Multiple:
Sum and Difference:
Additivity:

6. Rules for Definite Integrals
Max-Min Inequality: If max f and min f are the maximum and minimum values of f on [a, b], then
Domination:

7. Example Using the Rules for Definite Integrals
Suppose
Find
if possible.
Find
if possible.
Find
if possible.
Not enough information.

8. Average (Mean) Value Example Applying the Definition Use NINT
If f is integrable on [a, b], its average (mean) value on [a, b] is
Example Applying the Definition
Use NINT
Find the average value of on [0, 4].

9. The Mean Value Theorem for Definite Integrals
If f is continuous on [a, b], then at some point c in [a, b],

10. The Derivative of an Integral
This means that the integral is an antiderivative of f.
Set x = a

11. Pg. 290, 5.3 #1-35 odd