Chapter 7

Preview of Chapter 6

In this chapter we consider applications of integration. We will do
	areas between curves,
	volumes by rectangles,
	volumes by cylindrical shells,
	work, and
	average value of a function.
For each of these topics we will use integration to solve the problems.

Calculus 2 Lesson 6.1 Area between Curves

The following topics are the most important. Typical exercises from Calculus, 6^th edition, by James Stewart, are assigned at the end of each objective.

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

For each area, graph the functions and determine

whether the area approximation is basically vertical rectangles P352#1,5,7,9,13,15,23

whether the area approximation is basically horizontal rectangles P352 #11,19,21

the area using the Midpoint Rule P352-3#41,43,45

Before we can do our first Maple Assignment, we must install Maple and associate the worksheets with the software.

Maple Assignment: See Maple Assignment

When you are satisfied with your first Maple assignment, you'll need some information on Submitting Maple Assignments for a Grade.

Calculus 2 Lesson 6.2 Volume
The following topics are the most important. Typical exercises from Calculus, 6^th edition, by James Stewart, are assigned at the end of each objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1.	Define volume. Text
2.	Volume found by rotating an object about the x-axis. P362#1,3,7,19,23,27
3.	Volume found by rotating an object about the y-axis. P362#5,9,20,24,28
4.	Volume found by rotating an object about a line parallel to an axis. P362#11,13,15,17
5.	Volume found with slicing. P363#45,49,51,53,57
Maple Assignment: none

Calculus 2 Lesson 6.3 Volumes by Shells
The following topics are the most important. Typical exercises from Calculus, 6^th edition, by James Stewart, are assigned at the end of each objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1.	Give the definition of volume using cylindrical shells. Text
2.	Volume found by shells about the y axis. P368#3,5,7
3.	Volume found by shells about the x-axis. P368#9,11,13
4.	Volume found by shells about a line parallel to an axis. P368#15,17,19
5.	Find the volume using any method. P369#37-42
Maple Assignment: See Maple Assignment Submitting Maple Assignments for a Grade

Calculus 2 Lesson 6.4 Work
The following topics are the most important. Typical exercises from Calculus, 6^th edition, by James Stewart, are assigned at the end of each objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1.	For Work problems, know the following types:
1.a		definition of Force and Work as well as units; Text
1.b.		Find work when the force is constant; P373#1,2
1.c		Find work when the force varies; P373#3,4,5,6
1.d		Find work using Hooke's Law for springs; P373#7,9,11
1.e		Find work in cable problems; P373#13,14,15,16
1.f		Find work in water problems; P373#17,19,21,23
Maple Assignment: none

Calculus 2 Lesson 6.5 Average Value of a Function
The following topics are the most important. Typical exercises from Calculus, 6^th edition, by James Stewart, are assigned at the end of each objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1.	Find the average value of a function. P377#1,3,5,9,13,17,19
Maple Assignment: none