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 |
Solutions |
Riemann Sum Approximation(Left and Right Sums) |
Left and Right Sum Example |
Midpoint Sum Approximation |
Trapezoidal Sum Approximation |
2 |
The Definite Integral and Riemann Sums |
Lesson 2 |
Solutions |
Riemann Sums using Sumation Notation |
Riemann Sum using Summation Notation Example |
Evaluate a definite integral using a geometric formula (Video 1) (Video 2) (Video 3) |
3 |
Antidifferentiation & Indefinite Integration |
Lesson 3 |
Solutions |
Antiderivatives and Indefinite Integrals |
Reverse Power Rule(for antiderivatives) |
Integrals Containing Trigonometric Functions |
4 |
Differential Equations and Slope Fields |
Lesson 4 |
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 |
5 |
Applications Using the Definite Integral for Accumulation |
Lesson 5 |
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) |
6 |
The 1st and 2nd Fundamental Theorem of Calculus |
Lesson 6 |
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 |
7 |
The Mean Value Theorem for Integrals with AP Application |
Lesson 7 |
Solutions |
Average Value of a Function |
Calculating the Average Value over an Interval |
Mean Value Theorem for Integrals |