| Basic Integration and Applications of Accumulation |
| Day |
Notes |
Critical Homework |
Videos |
| 1 |
Area of a Region using Left, Right, Midpoint and Trapezoidal Sums
|
Lesson 1 Critical HW |
Solutions
|
Riemann Sum Approximation(Left and Right Sums) |
| Left and Right Sum Example |
| Midpoint Sum Approximation |
| Trapezoidal Sum Approximation |
| 2 |
The Definite Integral as a Riemann Sum
|
Lesson 2 Critical HW |
Solutions
|
Riemann Sums using Sumation Notation |
| Riemann Sum using Summation Notation Example |
| 3 |
Using Properties & Geometry to Evaluate Definite Integrals
|
Lesson 3 Critical HW |
Solutions
|
Evaluate a definite integral using a geometric formula (Video 1) (Video 2) (Video 3) |
| 4 |
Antidifferentiation & Indefinite Integration
|
Lesson 4 Critical HW |
Solutions
|
Antiderivatives and Indefinite Integrals |
| Reverse Power Rule(for antiderivatives) |
| Integrals Containing Trigonometric Functions |
| 5 |
The 1st and 2nd Fundamental Theorem of Calculus
|
Lesson 5 Critical HW |
Solutions
|
Fundamental Theorem of Calculus |
| 2nd Fundamental Theorem of Calculus |
| Basic Geometric Proof of the Fundamental Theorem of Calculus (Part 1), (Part 2) (Part 3) |
| 2nd Fundamental Theorem of Calculus Examples |
| 2nd Fundamental Theorem of Calculus Examples Requiring the Chain Rule |
| 6 |
Differential Equations and Slope Fields
|
Lesson 6 Critical HW |
Solutions
|
Slope Fields |
| Identifying a Slope Field for a Given Differential Equation |
| Graphing Specific Solutions to Differentials Using a Slope Field |
| Finding a Specific Solution to a Differential Equation |
| 7 |
Applications Using the Definite Integral for Accumulation
|
Lesson 7 Critical HW |
Solutions
|
Area Under Rate Function Gives the Net Change |
| Interpreting Definite Integral as Net Change |
| Motion Problems With Integrals: Displacement vs. Distance |
| AP Application Examples of the Definite Integral (EX 1), (EX 2), (EX 3), (EX 4), (EX 5), (EX 6) |
| 8 |
Applications of The Mean Value Theorem for Integrals & Average Value
|
Lesson 8 Critical HW |
Solutions
|
Average Value of a Function |
| Calculating the Average Value over an Interval |
| Mean Value Theorem for Integrals |
| |
Review for Unit 4 Major
Assessment
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Solutions
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