Unit 4:  Integrals

Unit 4:  Integrals

• Day 37:  Riemann Sums

  • • Video 1:  Math 251 vs Math 252

    • Video 2:  Finding Area with Three Subdivisions

    • Video 3:  Finding Area with Six Subdivisions

    • Video 4:  Thoughts About Delta x

    • Video 5:  Derivation of the LHS Formula

    • Video 6:  A Quick Lesson in French

    • Video 7:  LHS, RHS and MHS Formulas and Pictures

    • Video 8:  Final Example

      • • 5.1:  1a, 2, 3, 11, 13

          • • 13

        • Feel free to put this on your calculator:  LEFTSUM

• FriDay 38:  Three-Day Weekend (Math at least)

  • • The AP exam registration deadline is Monday, Nov 02, 2020. All students who are in an AP class, have registered for the AP exam in the College Board website AND have submitted a CV AP form for every AP exam they have registered for by the deadline, will have their exam fee paid by the school district. 

• MonDay 39:  The Definite Integral

  • • Video 1:  Definition of the Definite Integral

    • Video 2:  Bunch of Rules of Integrals

      • • 5.2:  5, 8, 9, 12, 30, 31, 33, 35, 41-43

          • • 33

• Day 40:  Evaluating Definite Integrals, an Introduction to FTC Part 2

  • • Video 1:  The Fundamental Theorem of Calculus?

    • Video 2:  Antiderivatives Again

    • Video 3:  Evaluating Some Definite Integrals

    • Video 4:  More Integration

    • Video 5:  Displacement vs. Total Distance

      • • 5.3:  1, 3, 15-33 odd, 42, 47, 52, 53

          • • 29 and 33 27 and 47 42

• Day 41:  The Fundamental Theorem of Calculus (this is sort of important)

  • • Video 1:  An Accumulated Value Function

    • Video 2:  The Fundamental Theorem of Calculus  (Part 1)

    • Video 3:  Example 2

    • Video 4:  Example 3

    • Video 5:  Example 4

    • Video 6:  Example 5

    • Video 7:  Example 6

      • • Did You See the Canvas Quizzes?

        • 5.4:  3-17 odd, 19abc

          • • 17 19

• Day 42:  Integration by Substitution Day 1

  • • Video 1:  Example 1

    • Video 2:  Example 2

    • Video 3:  Examples 3 and 4

    • Video 4:  Examples 5 and 6

    • Video 5:  Examples 7 and 8

    • Video 6:  Examples 9 and 10

    • Video 7:  Examples 11

      • • Are you all caught up with Canvas Quizzes?

        • 5.5:  7-32

          • • 20 27 31 and 32

• FriDay 43:  Integration by Substitution Day 2

  • • Video 1:  Using Substitution for Definite Integrals

    • Video 2:  Two More Examples

      • • 5.5:  37-52

          • • 43

            • 49 is a trick question like #52.  You'll never see problems like this, but they are "odd" functions so the answer is 0.  See Example 10 at the top of p. 395

• MonDay 44:  Integration by Parts

  • • Video 1:  New Formula and a "Proof"

    • Video 2:  Example 1

    • Video 3:  Example 2

    • Video 4:  Example 3

    • Video 5:  Example 4

    • Video 6:  Example 5

    • Video 7:  Example 6

    • Video 8:  Example 7

      • • 5.6:  3-23 odd, 41

          • • 7 and 17 21 23

            • 9 13 15

            • 19 41

• Day 45: Workday (click for semi-humorous pics)

  • • Video:  Stupid COVID

      • • Get Your Canvas Quizzes up to 100%

        • 
          

• Day 1:  New Stuff (wait... didn't we already do this?),  Other Integration Tricks 

  • • Video 1:  Riemann Recap

    • Video 2:  The Trapezoidal Rule

      • • READ 5.9

        • 5.9:  1, 2, 7ab, 13, 25 (with midpoint rule)

          • • 7 13 25

    • Video 3:  Using Trigonometric Identities

    • Video 4:  By Parts

    • Video 5:  Now What?  

    • Video 6:  Partial Fractions

    • Video 7:  Long Division (not on any tests)

      • • 5.7:  1-3, 5, 17-27 odd, 28

          • • 1 2 3 5

            • 21  At the Bottom when it says "Day 2 Videos", see Video 1 below

            • 23

• FriDay 2:  Archaic Integration (Never on ANY Test EVER)

  • • Video 1:  A New (Actually Really Old) Formula

    • Video 2:  There are a LOT of Archaic Formulas

    • Video 3:  Try 5.8:  #4

      • • 5.8:  1-11 odd, 17 (optional)... try at least one?  NOT on the test...

FRQ 9 Integration Techniques (No Calculator, Shoot for about 45 minutes)

FRQ 10 Reimann (No Calculator, Shoot for about 10 minutes)