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 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