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


Solutions

