Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Indefinite Integral (no limits) Definite Integral (has limits) Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Indefinite Integral (no limits) Definite Integral (has limits) Upper Limit (end) Limits give bounds and direction on a graph. On a graph, you travel from the lower limit to the upper limit. Lower Limit (start) 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Definite integrals can be used to represent the region between a function and the x-axis within the limits. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Area is always positive. But regions can have a negative value. When travelling left to right, regions above the x-axis are positive, while regions below the x-axis are negative. a<b 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

When travelling right to left, the signs are reversed. a>b Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. When travelling right to left, the signs are reversed. a>b 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Shade the region on the graph represented by the definite integral. Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Shade the region on the graph represented by the definite integral. Then evaluate the integral. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Find 2 values of “b” that make the definite integral true. Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Find 2 values of “b” that make the definite integral true. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Evaluate the definite integral. Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Evaluate the definite integral. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Are each of the following statements always, sometimes, or never true? Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Are each of the following statements always, sometimes, or never true? sometimes, ex. a=b always always sometimes 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Practice: Linear Geometric Definite Integration Worksheet Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. Practice: Linear Geometric Definite Integration Worksheet 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 4.2 Definite Integral as Geometric Area 13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals. 12/7/2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals