4 3 DEFINITE INTEGRAL 4 4 The Fundamental
- Slides: 22
4. 3 DEFINITE INTEGRAL 4. 4 The Fundamental Theorem of Calculus Dr. Halimah Alshehri Ø Definition of Definite Integral and Examples Ø Properties of Definite Integrals Ø Upper and lower bound Ø The Fundamental Theorem of Calculus. Ø the Mean Value Theorem. Ø Average Value of a Function.
Objectives: The main purpose for this lesson is to introduce the following: q q q q Evaluate a definite integral using limits. Evaluate a definite integral using properties of definite integrals. Evaluate an upper and lower bound. Evaluate a definite integral using the Fundamental Theorem of Calculus. Understand use the Mean Value Theorem for Integrals. Find the average value of a function over a closed interval. Understand use the Second Fundamental Theorem of Calculus. Dr. Halimah Alshehri
4. 3 DEFINITE INTEGRAL Dr. Halimah Alshehri
Notes : Dr. Halimah Alshehri
Method 1 Reimann sum (see book) Dr. Halimah Alshehri Method 2 o
Properties of the definite integral: 1 - Additive interval property Dr. Halimah Alshehri
Example: Evaluate by Using the Additive Interval Property Dr. Halimah Alshehri
Dr. Halimah Alshehri
3 - Definitions of Two Special Definite Integrals Dr. Halimah Alshehri
Dr. Halimah Alshehri
Dr. Halimah Alshehri
Dr. Halimah Alshehri
Dr. Halimah Alshehri
4. 4 The Fundamental Theorem of Calculus Dr. Halimah Alshehri
Dr. Halimah Alshehri
Dr. Halimah Alshehri
Dr. Halimah Alshehri
Dr. Halimah Alshehri
Theorem: (Mean Value Theorem for Integrals) Dr. Halimah Alshehri
Dr. Halimah Alshehri
Definition: (Average Value of a Function) Dr. Halimah Alshehri
Homework: 1, 3, 7, 9, 13, 15, 17, 23, 25, 27, 31, 43, 61, 67 7, 11, 15, 17, 23, 27, 29, 31, 33, 45, 51, 81 Dr. Halimah Alshehri