NAHS AP Calculus Unit 4

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