Blackboard Site

To access the Blackboard Learning System, visit rtnj.blackboard.com. Use your Student ID for User Name and Password. Look under Assignments for the Rectanglar and Trapezoidal Approximation folder.

Rectangular and Trapezoildal Approximation

Sums of rectangular areas are called Riemann Sums. In practice we choose one of three methods: Left-endpoint Rectangular Approximation Method, Right-endpoint Rectangular Approximation Method, or Midpoint Rectangular Approximation Method. Another method is called the Trapezoidal Rule. The midpoint method and the trapezoidal rule are brought out in the solutions to the Rectangular Approximation Method and the Trapezoidal Rule.

A few things to remember with these methods:

1. Widths won't always be one and they won't necessarily be the same for each sub-interval.

2. LRAM under approximates when the function is increasing and over approximates when the function is decreasing.

3. RRAM is the opposite. It over approximates when the function is increasing and under approximates when it is decreasing.

4. Trapezoids over approximate when the function is concave up, but under approximate when it is concave down. When a function is linear, trapezoids are an exact fit.


This example demonstrates LRAM and RRAM in a very simple context.

Applications of the Fundamental Theorem of Calculus (Practice Test)

Practice Test

Problem 1 Solution

Problem 1 Videos:
Part a-b
Part b-c
Part c

Problem 2 Solution

Problem 2 Videos:
Part a-b
Part c

Applications of the Fundamental Theorem of Calculus (Calculator Exercises)

Problem Set

Problem 1 Solution
Video 1 Parts a-c
Video 2 Part d

Problem 2 Solution
Video 1 Parts a-c
Video 2 Part d

Problem 3 Solution
Video 1 Parts a-c
Video 2 Parts c-d

Problem 4 Solution
Video 1 Parts a-c
Video 2 Parts d

Problem 5 Solution
Video 1 Parts a-c
Video Part d

Problem 6 Solution
Video

Midterm Review

AB Midterm Review Packet
You have not learned to do problem 31 yet, so it should not have been included.
Solutions

There will be 4 free response questions as well.
1) Conceptual Exercises on FTC
2) Increasing/Decreasing, Min/Max, Concave Up/Down, Points of Inflection
3) Implicit Differentiation
4) Motion (Calculator)

You must answer two of these.

Conceptual Exercises on the Fundamental Theorem of Calculus

These are the problems we worked on Friday in class. Solutions are also provided. This will be the last topic we discuss prior to mid-terms. Please try them and look at the solutions. We will talk about them again on Wednesday. I have also posted video solutions as well.

Exercises
Solutions

Videos:
Problem 1
Problem 2 Pt. 1
Problem 2 Pt. 2
Problem 2 Pt. 3
Problem 3
Problem 4 Pt. 1
Problem 4 Pt. 2
Problem 5

Basic Integration Problem Set and Solutions

Basic Integration FRQ Problem Set
Basic Integration FRQ Problem Set Solutions

Fundamental Theorem of Calculus Parts I & II

HW: Larson 7 Section 4.4 #5-31 odds, 35-39 odds, 41-51 odds, 75-91 odds

Area and Definite Integrals

HW: Larson 7 Section 4.3 #13-45

Antiderivatives and Indefinite Integration

HW: Larson 7 4.1 #1-41 odds, 55-61 odds