NAHS AP Calculus Unit 5

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