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N01 - Integral & Riemann Sums

Overview

N01 Standards Document

CALCULATOR OK FOR THIS STANDARD.

INTRODUCTION TO INTEGRAL CALCULUS

Khan Academy Video
​Motion Detection Lab (from Physics)
​
KEY - Motion Detection Lab (from Physics)
"WONDERS" (from Blue Period)
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RECOMMENDED PRACTICE
     TEXTBOOK 
  • Lesson 5.1 Exercises (pp278-283): 1, 2, 3, 6, 10, 17, 23, 26, 32, 37.
  • Lesson 5.2 Exercises (pp288-292): 1, 3, 5, 7, 9, 12, 18, 19, 22, 24, 25, 34, 37, 42, 60. 
  • Lesson 7.5 (pp376-385) Exercises: p382: 1-11 (odd). Lesson 7.5 includes much detail concerning numerical approximation of definite integrals - left, right, midpoint, and trapezoid rules.
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RECOMMENDED PRACTICE
  • ​Left and Right Riemann Sums
  • ​Accumulation of Change
  • Over and Under-Estimation
  • Midpoint & Trapezoidal Sums
  • (TOUGH) Riemann Sums in Summation Notation​
  • (TOUGH) Riemann Sums in Summation Notation

Objectives & Resources

1. Understand that the definite integral of a function over an interval is the limit of a Riemann sum over that interval and can be approximated using a variety of strategies. [EU 3.2]
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2. Be able to interpret the definite integral as the limit of a Riemann sum. Be able to express the limit of a Riemann sum in integral notation. [LO 3.2A, EK 3.2A3, EK 3.4A3]
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     a. Know that a Riemann sum, which requires a “partition” of an interval, is the sum of products, each of which is the value of the function at a point in a subinterval multiplied by the length of that subinterval of the partition. [EK 3.2A1]
     b. 
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These may help with 2b:

     Wolfram MathWorld: Riemann Sum Interactive Grapher/Calculator
     SUMMARY: Class Discussion of Riemann Sums and Definite Integral

Class Practice: Calculating Riemann Sums Exercise

     Calculating Riemann Sums Exercise
     KEY - Calculating Riemann Sums Exercise
     c.
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See TI Calculator Class Practice below as well as the Sample Content Assessment Items.
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EXPLORATION
APPROXIMATING AREA UNDER CURVE
  • DESMOS 1
  • DESMOS 2
  • DESMOS 3
Classwork: Desmos Intro to Riemann Sums
KEY - CW Desmos Intro to Riemann Sums

3. Using technology: Find definite integrals (correct to 3-decimal-places) using your TI calculator.

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There may be slight variations in how this works depending on your calculator model, but the basic three approaches in this video should work for you. Your calculator might produce a template like the one at right. If so, just use your arrow keys to move among the boxes. To calculate the definite integral at the left, just enter 0, 2, the function, and x in the corresponding locations, using arrow keys to move around.
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Class Practice: Using TI Calculator to Find Values of the Definite Integral                       KEY

SAMPLE CONTENT ASSESSMENT ITEMS

N01: Sample Assessment Items
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      • P09
      • P10
    • ALGEBRA 2 >
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