Learning Outcomes

1. Understand the relationship between the definite integral and net area.
2. Use geometry and properties of definite integrals to evaluate them.

Textbook

• Chapter 5.2  The Definite Integral

Textbook Assignment

• p. 545:    72, 73, 76, 77, 80, 81, 88, 89, 91, 93

WeBWork Assignment

• Integration-Definite

Exit problems of the session

1. Evaluate the integral using area formula: 2. Suppose that , , and , , find .

Key Concepts

• The definite integral is defined as the limit of a Riemann sum: .

It measures the net signed area of the region enclosed by , , , and • Properties of Definite Integral:    for constant  • Some definite integral can be evaluated by using areas of simple shapes, such as triangles, rectangles and circles.

#### Videos and Practice Problems of Selected Topics

1. Definite integral (4:51) Defining using Riemann sum.
2. Definite integral (2:28) Definite integrals represent the area between the curve of a function and the -axis.
3. Rewriting the limit of a Riemann sum as a definite integral (6:34) Write as a definite integral. (Optional)
4. Finding definite integrals using properties (2:08) Evaluate and using graphs.
5. * Practice: Finding definite integral using properties. (4 problems)
6. Definite integral on adjacent intervals (3:05) Explain the property: 7. Breaking up the integral’s interval (7:24) Evaluate definite integral with geometry.
8. Merging definite integrals over adjacent intervals (4:01) Evaluate definite integral using properties.
9. * Practice: Finding definite integral over adjacent intervals. (4 problems)