Calculus Approximating Area Using Riemann Sums with Lesson Video (Unit 6)
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Description
Approximating Area with Riemann Sums Lesson:
Your AP Calculus students will understand the "area under the curve" problem of calculus. They will explore left-hand sums, right-hand sums, midpoint sums, and the trapezoidal rule. These examples are presented in graphical, numerical, and tabular formats for rigor and variety.
What is included in this resource?
⭐ Guided Student Notes
⭐ Fully-editable SMART Board® Slides
⭐ Google Slides®
⭐ Homework/Practice assignment
⭐ Content quiz
⭐ Video Lesson Link for Distance Learning - Flipped Classroom models
⭐ Full solution set
Lesson Objective:
★ Use Left, Right, and Midpoint Riemann Sums and Trapezoidal Rule to estimate area under a curve.
College Board® Topics:
Topic 6.1: Exploring Accumulations of Change
Topic 6.2: Approximating Areas with Riemann Sums
College Board® Learning Objectives:
CHA-4: Definite integrals allow us to solve problems involving the accumulation of change over an interval.
CHA-4.A: Interpret the meaning of areas associated with the graph of a rate of change in context.
CHA-4.A.1 The area of the region between the graph of a rate of change function and the x-axis gives the accumulation of change.
CHA-4.A.2: In some cases, accumulation of change can be evaluated by using geometry.
CHA-4.A.3: If a rate of change is positive (negative) over an interval, then the accumulated change is positive (negative).
CHA-4.A.4: The unit for the area of a region defined by rate of change is the unit for the rate of change multiplied by the unit for the independent variable.
LIM-5: Definite integrals can be approximated using geometric and numerical methods.
LIM-5.A: Approximate a definite integral using geometric and numerical methods
LIM-5.A.1: Definite integrals can be approximated for functions that are represented graphically, numerically, analytically, and verbally.
LIM-5.A.2: Definite integrals can be approximated using a left Riemann sum, a right Riemann sum, a midpoint Riemann sum, or a trapezoidal sum; approximations can be computed using either uniform or nonuniform partitions.
LIM-5.A.3: Definite integrals can be approximated using numerical methods, with or without technology.
LIM-5.A.4: Depending on the behavior of a function, it may be possible to determine whether an approximation for a definite integral is an underestimate or overestimate for the value of the definite integral.
The unit includes:
1) Approximating Area With Riemann Sums
2) Sigma Notation and Riemann Sums
4) Properties of Definite Integrals
5) Antiderivatives & Indefinite Integration
6) The Fundamental Theorem of Calculus
7) Integration By Substitution
8) Integration of Transcendental Functions
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AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.
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