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 region, graph the functions and determine

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

P347

The definition of area in boxes 1 and 2 are important. Memorize them. Examples 1,2, and 3 should help you do your homework.

P347

The definition of area in box 3 is important. Memorize it. Example 5 should help you do your homework.

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

P351

Example 6 should help you do these exercises.

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

P349

Example 4 shows you how to do this.

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
	P355	The definition of the volume is given in the box on this page. Memorize it.
2.		Volume found by rotating an object about the x-axis. P362#1,3,7,19,23,27
	P355	Examples 1, 2 and 4 are useful.
3.		Volume found by rotating an object about the y-axis. P362#5,9,20,24,28
	P357	Example 3 is useful.
4.		Volume found by rotating an object about a line parallel to an axis. P362#11,13,15,17
	P358	Examples 5 and 6 are useful.
5.		Volume found with slicing. P363#45,49,51,53,57
	P360	Examples 7, 8 and 9 are useful.
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
	P365	The definition of the cylindrical shell is given as definition 1 at the bottom of the page.
	P366	The definition of volume using cylindrical shells is given in box 2 found in the middle of the page.
2.		Volume found by shells about the y axis. P368#3,5,7
	P366	Examples 1 and 2 are useful.
3.		Volume found by shells about the x-axis. P368#9,11,13
	P367	Example 3 is useful.
4.		Volume found by shells about a line parallel to an axis. P368#15,17,19
	P433	Example 4 is useful.
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
	P370	The definition of force is given as definition 1 at the top of the page. Memorize it.
	P370	The definition of work is given as definition 2 at the middle of the page. Memorize it.
	P370	Units for force and work in the metric and English system are given in the paragraph below definition 2 at the middle of the page. Memorize them.
1.b.		Find work when the force is constant; P373#1,2
	P370	Example 1 is useful.
1.c		Find work when the force varies; P373#3,4,5,6
	P371	The formula for work is given in box number 4. Memorize it.
	P371	Example 2 is useful.
1.d		Find work using Hooke's Law for springs; P373#7,9,11
	P371	Hooke's Law is given after Example 2. Memorize it
	P371	Example 3 is useful.
1.e		Find work in cable problems; P373#13,14,15,16
	P372	Example 4 is useful.
1.f		Find work in water problems; P373#17,19,21,23
	P371	Example 5 is useful.
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
	P375		The formula for the average value of a function is found in the box on the middle of the page. Memorize it.
	P375		Look at Example 1.
	P375		The Mean Value Theorem is given at the bottom of the page. Memorize it.
	P376		Use the Mean Value theorem to find the answer. Look at Examples 2 and 3.
Maple Assignment: none