Math 142, Chapter 7
Spring 2011
Zarestky
Chapter 7 Reading Notes
In this chapter, we will learn about a few selected applications of integration.
Section 7.1: Area Between Curves
By the end of this section, you should be able to:
• Calculate the area bounded between two curves.
To this point, we have interpreted the integral as the area between a curve and the x-axis. In this section,
you will explore areas bounded by two curves.
Make notes on Theorem 1 and the conceptual insights.
Work Example 1. This example should align with your previous experience. What questions do you have?
Work Example 2. Compare your answers to the book’s solution. What questions do you have?
Math 142, Chapter 7
Spring 2011
Zarestky
Work Example 3. Compare your answers to the book’s solution. What questions do you have?
Work Example 4. Compare your answers to the book’s solution. What questions do you have?
Work Example 5. Compare your answers to the book’s solution. What questions do you have?
We are not going to cover example 6 nor the Income Distribution application. Skip ahead to the exercises.
Check your understanding of this section by working a few problems from the exercises on your own.
Focus on 1-4, 7-33(odd), 37-55(odd), 63, 65, 67, 79, 81.
Do you have any questions?
Math 142, Chapter 7
Spring 2011
Zarestky
Section 7.2: Applications in Business and Economics
By the end of this section, you should be able to:
• Calculate the consumers’ and producers’ surplus, given supply and demand curves.
In this section, we will focus exclusively on consumers’ and producers’ surplus. Skip ahead to the bottom
of p. 426. Read the introductory paragraph and the definition of consumers’ surplus and make notes for
yourself.
Work Example 4. Compare your answers to the book’s solution. What questions do you have?
Producers’ surplus is very similar to consumers’ surplus. Again, make notes on the definition for yourself.
Work Example 5. Compare your answers to the book’s solution. What questions do you have?
Math 142, Chapter 7
Spring 2011
Zarestky
In example 6, you will use the equilibrium price and quantity.
Work Example 6. Compare your answers to the book’s solution. What questions do you have?
Check your understanding of this section by working a few problems from the exercises on your own.
Focus on 43-54.
What questions do you still have?