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Unit 5 - Integration
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Date

Classwork

Homework

MAKE SURE YOU ARE SIGNED IN TO YOUR KHAN ACADEMY ACCOUNT BEFORE WATCHING THE VIDEOS!

Learning Objectives

Thu

Fri

Feb 19,20

HW 5.1 assigned  (DUE: Mon Feb 23)

Simple Riemann approximation using rectangles (6:44)

Approximating area under curve and sigma notation (7:06)

Riemann sum when function is negative (6:35)

Answer this survey by 7am Monday as part of your HW grade

Questions you should be able to answer

  • What does a Riemann sum calculate?
  • What is Δx (delta x)?
  • How does sigma (Σ) notation work?
  • What is the difference between a left-hand Riemann sum and a right-hand Riemann sum?
  • Can a Riemann sum be negative? Explain.

Mon

Feb 23

HW 5.1 DUE

CW 5.1

Left, right, & midpoint Riemann sums

(this CW worksheet is NOT homework - finish during class Tues/Wed)

HW 5.2 assigned  (DUE: Thu/Fri) ← postponed: sub

Rectangular and trapezoidal Riemann approximations (8:12)

Trapezoidal approximation of area under a curve (8:26)

Answer this survey by 7am the day HW 5.2 is due as part of your HW grade

Video: notes for the CW worksheet

(do this during class on Tues/Wed)

Questions you should be able to answer

  • How is a midpoint Riemann sum SIMILAR to a left or right Riemann sum?
  • How is a trapezoidal Riemann sum DIFFERENT from left, right, and midpoint Riemann sums?
  • Which of the four types of Riemann sums is the most accurate?

Tue

Wed

Feb 24,25

(sub)

Finish CW 5.1

CW 5.2

Trapezoidal sums & integral notation

NOTES for CW 5.2

HW 5.3 assigned  (DUE: Mon)

   (worksheet, handed out in class)

Thu

Fri

Feb 26,27

HW 5.2 DUE

Finish CW 5.2

No new HW - complete HW 5.3

Mon

Mar 2

HW 5.3 DUE

CW 5.3

Integration on the calculator (bugs)

Start CW 5.4 (p7)

Indefinite integration, part 1

HW 5.4 (Riemann Sum check-in) assigned  (DUE: Tue/Wed)

Tue

Wed

Mar 3,4

Check-in DUE

Finish CW 5.3 (p2)

CW 5.4

Indefinite integration, part 1

Whiteboard integration practice

HW 5.5 assigned  (DUE: Thu/Fri)

Choose one of the options below (do both if you have the time).

Option 1:

If integration makes sense to you, do this survey.  Make sure you also understand the answers to the questions at the right.

Survey - answer by 7am on the due date

Option 2:

If you were absent, or if you didn’t understand what we did in class, please watch these Khan Academy videos & take notes.  Make sure you understand the answers to the questions at the right.  (Then try the survey if you have time!)

Antiderivatives and indefinite integrals (3:43)

Indefinite integrals of x raised to a power (5:48)

Antiderivative of x^-1 (7:35)

Basic trig and exponential antiderivatives (4:04)

Antiderivative of hairier expression (6:16)

Questions you should be able to answer

  • What is an antiderivative?
  • How can I find the antiderivative of x^n?
  • How can I find the antiderivative of 1/x, e^x, and trig expressions?
  • What can I do to simplify expressions before I take the antiderivative?

Thu

Fri

Mar 5,6

HW 5.5 DUE

CW 5.5

The Fundamental Theorem of Calculus

HW 5.6 assigned  (DUE: Mon)

Optional:

 Fundamental Theorem of Calculus (8:02)

 Connecting the first and second fundamental theorems of calculus (4:44)

Required:

Fundamental Theorem of Calculus practice

 Calculating average value of function over interval (5:08)

 Mean Value Theorem for integrals (9:06)

Mon  Tue

Mar 9,10

HW 5.6 DUE

CW 5.6

MVT & average value

HW 5.7 assigned  (DUE: Tue/Wed)

 U-substitution (5:11)

 U-substitution example 2 (4:04)

 U-substitution example 3 (5:33)

 U-substitution with ln x (3:39)

Now SUMMARIZE at the end of your notes (write a small paragraph):  What are the key components of u-substitution?  How does it work?  This is part of your HW grade!

Wed Thu

Mar 11,12

HW 5.7 DUE

CW 5.7

U-substitution

HW 5.8 assigned  (DUE: Fri/Mon(2nd))

worksheet, handed out in class

Fri

(7th period)

Mar 13

HW 5.8 DUE

CW 5.8

U-substitution: change of variables

HW 5.9 assigned  (DUE: Wed)

worksheet, handed out in class

2nd period

7th period

Mon

Mar 16

HW 5.8 DUE

CW 5.8

U-substitution: change of variables

HW 5.9 assigned  (DUE: Tue)

worksheet, handed out in class

Mon

Mar 16

CW 5.9

Differential equations: general & particular solutions

CW 5.9 assigned  (DUE: Wed)

worksheet, handed out in class

Tue

Mar 17

HW 5.9 DUE

CW 5.9

General & particular solutions

HW 5.9 assigned  (DUE: Thu)

worksheet, handed out in class

Wed

Mar 18

CW 5.10

Differential equations: slope fields

HW 5.11 assigned  (DUE: Wed)

worksheet, handed out in class

Thu

Mar 19

HW 5.9 DUE

CW 5.10

Differential equations: slope fields

HW 5.11 assigned  (DUE: Tue)

worksheet, handed out in class

Fri

Mar 20

HW 5.11 DUE

CW 5.12

Area between curves

HW 5.13 assigned  (DUE: Wed)

worksheet, handed out in class

Spring Break!

Unit 4 Test correction instructions & hints   (due Thursday, April 8)

2nd period

7th period

Mon

Mar 30

Finish CW 5.10

Differential equations: slope fields

Mon

Mar 30

CW 5.14

Free response practice

HW 5.15 assigned  (DUE: Wed)

worksheet, handed out in class

(allow 15 min per problem - finish CW 5.14 and HW 5.15)

Tue

Mar 31

HW 5.11 DUE

CW 5.12

Area between curves

CW 5.14

Free response practice (front only)

HW 5.13 assigned  (DUE: Thu)

worksheet, handed out in class

(Also finish CW 5.12, and FRONT of CW 5.14)

Wed

Apr 1

HW 5.15 DUE

AP Warmup #1

Answers to free response practice

Start CW 5.16

Volume by rotation (disk, washer)

HW 5.17 assigned  (DUE: Fri Mon)

worksheet, handed out in class

Thu

Apr 2

HW 5.13 DUE

AP Warmup #1

Answers to free response practice

CW 5.16

Volume by rotation (disk, washer)

CW 5.14 (back) & HW 5.15 assigned  (DUE: Mon)

worksheets, handed out in class

Fri

Apr 3

HW 5.17 DUE

AP Warmup #2 (front)

CW 5.16

Volume by rotation (disk, washer)

Finish CW 5.16 & HW 5.17  (DUE: Mon)

worksheets, handed out in class

The videos in Khan Academy’s Solids of Revolution - disc method section might help if you are having trouble, especially:

Unit 4 Test correction instructions & hints   (due Thursday, April 8)

2nd period

7th period

Mon

Apr 6

CW 5.14, HW 5.15 DUE

Go over CW 5.14, HW 5.15 answers

Continue CW 5.16

HW 5.17 assigned  (DUE: Tue)

worksheet, handed out in class

The videos in Khan Academy’s Solids of Revolution - disc method section might help if you are having trouble, especially:

Mon

Apr 6

CW 5.16, HW 5.17 DUE

CW 5.18

Volume on a base

AP Warmup #2 (back)

HW 5.19 assigned  (DUE: Wed)

worksheet, handed out in class

The following Khan Academy videos might help if you are having trouble:

Tue

Apr 7

HW 5.17 DUE (can turn in Thurs if you made progress but had more questions)

AP Warmup #2 (front)

Finish CW 5.16

Finish HW 5.17 (DUE: Thu)

Wed

Apr 8

HW 5.19 DUE (can turn in Mon if you made progress but had more questions)

AP Warmup #2 (back)

Finish CW 5.18

Volume on a base

Unit 4 test corrections due Thurs!

HW 5.20 assigned (DUE: Mon)

Watch and take notes on the following Khan Academy videos:

 Disc method around y-axis (7:33)

 Disc method rotating around vertical line (4:50)

 Washer or ring method for vertical line rotation (7:50)

Thu

Apr 9

HW 5.17 DUE

AP Warmup #2 (back)

CW 5.18

Volume on a base

Unit 4 test corrections due!

HW 5.19 assigned (DUE: Mon)

worksheet, handed out in class

HW 5.20 assigned (DUE: Mon)

Watch and take notes on the following Khan Academy videos:

 Disc method around y-axis (7:33)

 Disc method rotating around vertical line (4:50)

 Washer or ring method for vertical line rotation (7:50)

Fri

Apr 10

No school - grading day

End of 3rd Quarter

2nd period

7th period

Mon

Apr 13

HW 5.20 DUE

Mixed volume review

HW 5.21 assigned (DUE: Tues)

Watch and take notes on the following Khan Academy videos:

 Shell method for rotating around vertical line (5:32)

 Shell method with two functions of x (4:11)

Mon

Apr 13

HW 5.20 DUE

Mixed volume review

HW 5.21 assigned (DUE: Wed)

Watch and take notes on the following Khan Academy videos:

 Shell method for rotating around vertical line (5:32)

 Shell method with two functions of x (4:11)

Tue

Apr 14

HW 5.21 DUE

CW 5.22

Volume (y, shell)

HW 5.23 assigned (DUE: Mon)

volume of edible solids worksheet

Wed

Apr 15

HW 5.21 DUE

CW 5.22

Volume (y, shell)

HW 5.23 assigned (DUE: Mon)

volume of edible solids worksheet

Thu

Apr 16

Formula sheet

CW 5.22

HW: finish HW 5.23 worksheet

Fri

Apr 17

Formula sheet

CW 5.22

HW: finish HW 5.23 worksheet

2nd period

7th period

Mon

Apr 20

HW 5.23 DUE

Slope field matching

AP Review - CW 6.1

HW 6.2 assigned (DUE: Tues)

Mon

Apr 20

HW 5.23 DUE

AP Warmup #3

Slope field matching

AP Review - CW 6.1

HW 6.2 assigned (DUE: Wed)

Tue

Apr 21

HW 6.1 DUE - slope fields

AP Warmup #3

AP Warmup #4

AP Review

- CW 6.1: slope fields

- Notes: exponential growth

HW 6.3 assigned (DUE: Thurs)

Wed

Apr 22

HW 6.1 DUE - slope fields

AP Warmup #4

AP Review

- CW 6.1: slope fields

- Notes: exponential growth

HW 6.3 assigned (DUE: Fri)

Thu

Apr 23

HW 6.3 DUE - tables / Riemann sums / integration

AP Warmup #5

AP Review

- finish CW 6.1: slope fields

- CW 6.3: tables / Riemann sums / integration

Analyze Multiple Choice practice test problems

HW 6.5 assigned (DUE: Mon)

Fri

Apr 24

HW 6.3 DUE - tables / Riemann sums / integration

AP Warmup #5

AP Review

- CW 6.3: tables / Riemann sums / integration

Analyze Multiple Choice practice test problems

HW 6.5 assigned (DUE: Mon)

2nd period

7th period

Mon

Apr 27

HW 6.5 DUE - analyzing a graph

AP Warmup #6

Go over HW 6.5

HW 6.6 assigned (DUE: Tues)

Mon

Apr 27

HW 6.5 DUE - analyzing a graph

AP Warmup #6

Go over HW 6.5

HW 6.6 assigned (DUE: Wed)

Tue

Apr 28

HW 6.6 DUE - volume & area   **ACT test (juniors)**

AP Warmup #7

Go over HW 6.6

CW 6.8

Theorem practice: MVT / IVT

Finish CW 6.8 (DUE: Thurs)

Wed

Apr 29

HW 6.6 DUE - volume & area

AP Warmup #7

Go over HW 6.6

Analyze Free Response practice test problems

HW 6.7 assigned (DUE: Fri)

Thu

Apr 30

CW 6.8 DUE - MVT/IVT

AP Warmup #8

Go over CW 6.8

Analyze Free Response practice test problems

Testing advice

HW 6.7 assigned (DUE: Mon)

STUDY - MEMORIZE - REVIEW

Fri

May 1

HW 6.7 DUE - particle motion

AP Warmup #8

Go over HW 6.7

CW 6.8

Theorem practice: MVT / IVT

Testing advice

Finish CW 6.8 (DUE: Mon)

STUDY - MEMORIZE - REVIEW

2nd period

7th period

Mon

May 4

HW 6.7 DUE - particle motion

AP Warmup #9

Go over HW 6.7

Last minute review / questions

STUDY - MEMORIZE - REVIEW

Good luck!!!!

Mon

May 4

CW 6.8 DUE - MVT/IVT

AP Warmup #9

Go over CW 6.8

Last minute review / questions

STUDY - MEMORIZE - REVIEW

Good luck!!!!

Tue

May 5

AP Calculus Test

Wed

May 6

Review for Unit 5 test

Thu

May 7

Review for Unit 5 test - PART 1

Review

Answers

Fri

May 8

Review for Unit 5 test - PART 1

Review

Answers

2nd period

7th period

Mon

May 11

Review for Unit 5 test - PART 2

Review

Answers

Mon

May 11

Review for Unit 5 test - PART 2

Review

Answers

Tue

May 12

Review for Unit 5 test - PART 3

Review

Answers

Wed

May 13

Review for Unit 5 test - PART 3

Review

Answers

Thu

May 14

Review for Unit 5 test - PART 4

Review

Answers

Fri

May 15

Review for Unit 5 test - PART 4

Review

Answers

2nd period

7th period

Mon

May 18

Review for Unit 5 test - PART 4

Review

Answers

Mon

May 18

Review for Unit 5 test - PART 4

Review

Answers

Tue

May 19

Review for Unit 5 test - PART 5

Review

Answers

Wed

May 20

Review for Unit 5 test - PART 5

Review

Answers

Thu

May 21

Review for Unit 5 test - PART 6

Review

Answers

Fri

May 22

Review for Unit 5 test - PART 6

Review

Answers

2nd period

7th period

Mon

May 25

NO SCHOOL

STUDY!!!

Review  Answers

Mon

May 25

NO SCHOOL

STUDY!!!

Review  Answers

Tue

May 26

UNIT 5 TEST

Wed

May 27

UNIT 5 TEST

Thu

May 28

In-class projects

Fri

May 29

In-class projects

2nd period

7th period

Mon

June 1

In-class projects

Mon

June 1

In-class projects

Tue

June 2

Projects

Seniors - last day!

Wed

June 3

Projects

Seniors - last day!

Thu

June 4

In-class projects

Fri

June 5

In-class projects

2nd period

7th period

Mon

June 8

In-class projects

Mon

June 8

In-class projects

Tue

June 9

In-class projects

Wed

June 10

In-class projects

Thu

June 11

In-class projects

Fri

June 12

In-class projects