Basic Integration and Applications of Accumulation |
Day |
Notes |
Critical Homework |
Videos |
1 |
Area of a Region using Left, Right, Midpoint and Trapezoidal Sums

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Lesson 1 Critical HW |
Solutions

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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

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Lesson 2 Critical HW |
Solutions

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Riemann Sums using Sumation Notation |
Riemann Sum using Summation Notation Example |
3 |
Using Properties & Geometry to Evaluate Definite Integrals

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Lesson 3 Critical HW |
Solutions

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Evaluate a definite integral using a geometric formula (Video 1) (Video 2) (Video 3) |
4 |
Antidifferentiation & Indefinite Integration
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Lesson 4 Critical HW |
Solutions

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Antiderivatives and Indefinite Integrals |
Reverse Power Rule(for antiderivatives) |
Integrals Containing Trigonometric Functions |
5 |
The 1st and 2nd Fundamental Theorem of Calculus

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Lesson 5 Critical HW |
Solutions

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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
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Lesson 6 Critical HW |
Solutions

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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
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Lesson 7 Critical HW |
Solutions

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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

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Lesson 8 Critical HW |
Solutions

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Average Value of a Function |
Calculating the Average Value over an Interval |
Mean Value Theorem for Integrals |
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Review for Unit 4 Major
Assessment
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Solutions

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