- Understand the relationship between the definite integral and net area.
- Use geometry and properties of definite integrals to evaluate them.
- Chapter 5.2 The Definite Integral
- p. 545: 72, 73, 76, 77, 80, 81, 88, 89, 91, 93
Exit problems of the session
Evaluate the integral using area formula: .
- Suppose that , , and , , find
- 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:
- 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
- Definite integral (4:51) Defining using Riemann sum.
- Definite integral (2:28) Definite integrals represent the area between the curve of a function and the -axis.
- Rewriting the limit of a Riemann sum as a definite integral (6:34) Write as a definite integral. (Optional)
- Finding definite integrals using properties (2:08) Evaluate and using graphs.
- * Practice: Finding definite integral using properties. (4 problems)
- Definite integral on adjacent intervals (3:05) Explain the property:
- Breaking up the integral’s interval (7:24) Evaluate definite integral with geometry.
- Merging definite integrals over adjacent intervals (4:01) Evaluate definite integral using properties.
- * Practice: Finding definite integral over adjacent intervals. (4 problems)