Math 192   Calculus 2

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Preview of Chapter 6
A student completing this chapter successfully will be able to:
bulletGraph regions bounded by curves and use the definite integral to find exact area.
bulletRevolve regions about an axis and use the definite integral to find exact volume by methods of disks and shells.
bulletUse the definite integral to find the work done in spring, pumping and cable problems.
bulletDemonstrate the Mean Value Theorem for Integrals.

6.1        6.2        6.3        6.4        6.5

Calculus 2        Lesson 6.1       Area between Curves
The following topics are the most important. Typical exercises from Calculus, 7th edition Early Transcendentals, 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
a. whether the area approximation is basically vertical rectangles P427#1,5,7,9,13,15,23
P422 The definition of area in boxes 1 and 2 are important. Memorize them. Examples 1,2, and 3 should help you do your homework.
  P423 Watch the video from the link in the ebook.
  P425 The definition of area in box 3 is important. Memorize it. Example 5 should help you do your homework.
  P425 Watch the video from the link in the ebook.
b. whether the area approximation is basically horizontal rectangles P427 #3,11,17,19
P426 Example 6 should help you do these exercises.
  P426 Watch the video from the link in the ebook.
c. the area using the Midpoint Rule P428#43,45,47
P424 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,  7th edition Early Transcendentals, 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
P431 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. P438#1,3,7,19,23,27
P431 Examples 1, 2 and 4 are useful. 
  P432 Watch the video from the link in the ebook.
3. Volume found by rotating an object about the y-axis. P438#5,9,20,24,28
P433 Example 3 is useful.
  P433 Watch the video from the link in the ebook.
4. Volume found by rotating an object about a line parallel to an axis.  P438#11,13,15,17
P434 Examples 5 and 6 are useful.
5. Volume found with slicing. P439#43,45,47,49,51,53,55
P436 Examples 7, 8 and 9 are useful.
  P437 Watch the video from the link in the ebook.
Maple Assignment: none

 

Calculus 2        Lesson 6.3      Volumes by Shells
The following topics are the most important. Typical exercises from Calculus, 7th edition Early Transcendentals, 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
P441 The definition of the cylindrical shell is given as definition 1 at the bottom of the page.
P442 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. P445#3,5,7
P443 Examples 1 and 2 are useful.
  P443 Watch the video from the link in the ebook.
3. Volume found by shells about the x-axis. P445#9,11,13
P443 Example 3 is useful.
  P443 Watch the video from the link in the ebook.
4. Volume found by shells about a line parallel to an axis. P445#15,17,19
P444 Example 4 is useful.
  P444 Watch the video from the link in the ebook.
5. Find the volume using any method. P445#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, 7th edition Early Transcendentals, 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
P446 The definition of force is given as definition 1 at the middle of the page. Memorize it.
P446 The definition of work is given as definition 2 at the bottom of the page. Memorize it.
  P446 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; P449#1,2
P446 Example 1 is useful.
  P446 Watch the video from the link in the ebook.
1.c Find work when the force varies; P449#3,4,5,6
  P447 The formula for work is given in box number 4. Memorize it.
P447 Example 2 is useful.
1.d Find work using Hooke's Law for springs; P450#7,9,11
P447  Hooke's Law is given after Example 2. Memorize it
  P448 Example 3 is useful.
  P448 Watch the video from the link in the ebook.
1.e Find work in cable problems; P450#13,14,15,16
P448 Example 4 is useful.
  P448 Watch the video from the link in the ebook.
1.f Find work in water problems; P450#17,19,21,23
P448 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, 7th edition Early Transcendentals, 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. P453#1,3,5,9,13,17,19
  P452 The formula for the average value of a function is found in the box at the top of the page. Memorize it.
P452 Look at Example 1. 
  P452 Watch the video from the link in the ebook.
  P452  The Mean Value Theorem is given at the bottom of the page. Memorize it.
  P452 Use the Mean Value theorem to find the answer. Look at Examples 2 and 3.
  P452 Watch the video from the link in the ebook.
  P453 Watch the video from the link in the ebook.
Maple Assignment:  none