Integration - changes are in red!
Websites to help you with Chapter 6
Print Version of this syllabus - MS Word
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Extra Credit
Opportunity NOTE: AMC will be
given on February 6th in the cafeteria - hours 1 and 2 for Extra Credit! |
| Monday,
January 22 |
Review - Get up to speed on derivatives.... |
Homework: Finish corrections on the chapter 5
exams - Take-home and in-class
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Tuesday, January 23 |
6.1 What is an Integral? |
Objectives: You will be able to:
- define definite and indefinite integrals
- make a connection between velocity and time as
area under a curve, graphically
- approximate distance traveled (area under a
curve) over an interval of time
Homework: Read p. 361 - 371 and take notes.
Do page 372 # 1 - 7 odds (use average velocity over the interval to
approximate) and # 11 - 20
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NOTES and HOMEWORK will be very important this chapter
because there will be numerous homework and notes quizzes during the
chapter!
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Wednesday, January 24 |
6.1 Area under a curve and
summation notation |
Objectives: You will be able to:
- write and expand the summation notation for a
function/graph
ACTIVITY:
Quiz over derivatives
Homework: Review notes on section 6.1. Do page 374 # 21 - 35 odds
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include graphs for each problem, shading the region
that you are finding the area of.
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HIH - Hand-in Homework - due Friday, 1/26
Read the historical notes on pi on
pages 275 - 379 and write a 1-2 paragraph reflection on these notes
and how they relate to the concept of an integral. Put your
reflection on a separate piece of paper to turn in.
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Thursday, January 25 |
6.1 Area under a curve and
summation notation |
Objectives: You will be able to:
- write and expand the summation notation for a
function/graph
Homework: Review notes on section 6.1.
Do page 375 # 37 - 49 odds
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HIH - Hand-in Homework - due Monday, 1/29
P. 373 # 22, 24, 26, 34, 36, 42, 48 |
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Friday, January 26 |
Riemann Sums - Investigation with Geometer's Sketchpad! |
Objectives: You will be able to:
- understand and use integral notation - integrand,
limits of integration, and variable of integration
- understand a Riemann sum, regular partitions,
subintervals, and what it means for an integral to be Riemann integrable
ACTIVITY: Worksheet on Riemann Sums - Due
Wednesday, 1/31
Homework: Read and take notes on p. 375 -391 and do p. 391 # 1-3,
5, 6, and 9 - 16
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Monday, January 29 |
6.2 Defining and
Computing Definite Integrals |
Objectives: You will be able to:
- find partition points and calculate upper and
lower Riemann sums for definite integrals
Review notes on 6.2 and do p 392 # 17 - 28 all
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Tuesday, January 30 |
6.2 Defining and
Computing Definite Integrals - cont. |
Objectives: You will be able to:
- calculate the worst error of an approximation of
an integral
- understand and use the constant multiple property
(theorem 6.1), the additive function property (theorem 6.2), additivity
over intervals (theorem 6.3), and the comparison property (theorem 6.4)
- explore graphs to calculate definite integrals
over intervals
Homework: Reread 6.2 (pages 386 - 391) and
review your notes. Do p. 392 # 29 - 35 odds
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Wednesday, January 31
** Riemann Sum Lab Due Today |
QUIZ
over 6.1 - 6.2 |
Homework: Read and take notes on 6.3 (p. 396 - 401). Be able
to define ANTIDERIVATIVE
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Thursday, February 1 |
6.3 What is an
Antiderivative? What are slope fields? |
Objectives: You will be able to:
- generate graphs of slope fields with a calculator
- relate velocity graphs back to distance traveled
graphs
- draw slope fields (direction fields) from graphs
of derivatives
Activity: PowerPoint on Slope Fields and
Antiderivatives
Homework: Review your notes on 6.3 and do
slope field worksheet
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Friday, February 2 |
6.4 Computing
Indefinite Integrals |
Objectives: You will be able to:
- compare and contrast area graphs and slope fields
- connect area graphs and slope fields to
antiderivatives
- know the integrals given in this section (quiz
on these and slope fields on Monday!)
Homework: Read and take notes on 6.4 (pages
405 - 413 ) and do p. 402 #21 - 28 and
p. 413 # 1 - 15 odds and learn the integrals in this
section for a
quiz on Wednesday.
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Monday, February 5 |
6.4 Computing
Indefinite Integrals |
QUIZ
over
Derivatives with domains of trig
functions (was scheduled for Friday, but was postponed!)
- non replaceable
Objectives: You will be able
to:
- know and use the properties of antiderivatives
- realize the consequences of the mean value
theorem with integrals
- graph area functions and create tables of values
using your calculator's integrator
Homework: Review your notes on page 414 #
17, 19, 21, 22 -
25, and 27 - 32
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| Tuesday,
February 6 |
6.5 Fundamental
Theorems of Calculus I and II
American High School Math Exam
Cafeteria - 1st and Second Hours |
Objectives: You will be able to:
- know the connection between integral and
differential Calculus
- use the First and Second Fundamental Theorems of
Calculus in definite and indefinite integrals
Homework: Read and take notes on 6.5 (pages 416
- 425), write a one page paper describing in your own words the controversy
discussed in the section, and do p. 425 # 1 - 21 odds
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| Wednesday,
February 7 |
6.6 Numerical
Integration Techniques
2nd INTEGRAL Quiz with u's and du's and
Slope Fields |
Objectives: You will be able to:
- graph the area functions for definite integrals
and then graph the derivative of each area function and compare it to
the original function's graph
- to use Left, right Midpoint, Trapezoidal, and
Simpson's Rules to find approximations of integrals
Homework: Read and take notes on section 6.6
(pages 428 – 438), do p. 426 # 23-27 odds, and p. 438 # 1, 3,
and 5 (do 2 and 4 partitions by hand and use your calculator for 8, 16,
and 32 partitions).
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| Thursday,
February 7 |
6.6 Numerical
Integration Techniques (cont.)
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Objectives: You will be able to:
- graph the area functions for definite integrals
and then graph the derivative of each area function and compare it to
the original function's graph
- to use Left, right Midpoint, Trapezoidal, and
Simpson's Rules to find approximations of integrals
Homework: Review notes on section 6.6,
do p. 438 # 7, 9, and 11 (do 2 and 4 partitions by hand and use your
calculator for 8, 16, and 32 partitions) and work on HIH due Tuesday
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HIH - Hand-in Homework - due
Tuesday, 2/13
Page 438 # 4 and 10 - show all work for 2 and 4 partitions including a
graph for each showing partition points, appropriate rectangles/trapezoids
for each of the first four methods. You can use the same graph and
color code each method if you wish. You may use your calculator for
the other partitions of 8, 16, and 32. (Make sure to enter each
function properly!)
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Friday, February 8
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NO School - School Improvement Day
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Monday, February 12
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NO
School - Lincoln's Birthday
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Tuesday, February 13 |
NO
School - Snow Day |
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Wednesday, February 14 |
NO
School - Snow Day |
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| Thursday,
February 15 |
6.6 Numerical
Integration Techniques (cont.)
QUIZ
over
Derivatives and integrals - non
replaceable |
Group
Activity - Lab points
Homework: P. 438 # 13 - 16 all and use your calculator to find
answers to #17 - 20, and do 21-27 odds
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| Friday, February 16 |
6.7
Methods of Integration |
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Objectives: You will be able to:
- use substitution as a method of solving
indefinite integrals
- use substitution to find the general
antiderivatives of functions
- use the substitution technique to help in
recognizing a derivative produced by the chain rule.
Homework: Read and take notes on section 6.7
(pages 444 - 453) and do p. 453 # 1 - 19 odds
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| Monday, February 19 |
6.7 Methods of
Integration - continued |
Objectives: You will be able to:
- use substitution as a method of solving
indefinite integrals
- use substitution to find the general
antiderivatives of functions
- use the substitution technique to help in
recognizing a derivative produced by the chain rule.
Homework: Review your notes on section 6.7 and
do p. 453 # 21 - 49 odds
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| Tuesday, February
20 |
6.7 Methods of
Integration
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Objectives: You will be able to:
- use substitution as a method of solving
indefinite integrals
- use substitution to find the general
antiderivatives of functions
- use the substitution technique to help in
recognizing a derivative produced by the chain rule.
Homework: Review your notes on section 6.7
(pages 444 - 453) and do p. 453 # 51 - 55 and take-home test
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| Wednesday, February
21 |
REVIEW -
Chapter 6 |
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Thursday, February 22 |
REVIEW -
Chapter 6
Quiz
over chapter 6
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| Friday, February
23 |
REVIEW -
Chapter 6 |
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| Monday, February 26 |
-
Take-Home Test
Due today
-
In-Class TEST
today!
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| Homework:
On three 4" x 6" Note cards, choose
and write 3 problem/questions from chapter 6 on the front
of each of the cards. On the back, write complete solutions.
Choose the problems that you’d most like to remember for the AP
exam. We are continuing our review now while the material is
fresh in your minds. |
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Websites that might be helpful
this chapter….
True/False test for Integrals :
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/c5.html
Review Problems:
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Calcquestintegral.html
Find the Integrals:
http://www.efunda.com/math/integrals/integrals.cfm
The Integrator: http://integrals.wolfram.com/index.jsp
WebMath Integration Notes:
http://www.webmath.com/Integrals/integrals.html
Integrals at:
http://www.math.com/tables/integrals.htm
Tools for Integration from Vanderbilt:
http://www.math.vanderbilt.edu/~pscrooke/toolkit.integrals.html
Yahoo Education – HotMath Practice Problems with tutor
help available…
http://education.yahoo.com/homework_help/math_help/problem_list?id=minicalcgt_5_1
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