Calculus Properties of Definite Integrals with Lesson Video (Unit 6)
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Description
Applying Properties of Definite Integrals Lesson:
Your AP Calculus students will understand and evaluate a definite integral using properties of definite integrals. They will find area under a curve using geometric formulas.
***(2/18/2022) corrected homework key question 21 to show negative sign only covers area under the x-axis.
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 properties of integrals and geometric formulas to approximate area under a curve.
College Board® Topics:
Topic 6.6: Applying Properties of Definite Integrals
College Board® Learning Objectives:
FUN-6: Recognizing opportunities to apply knowledge of geometry and mathematical rules can simplify integration.
FUN-6.A: Calculate a definite integral using areas and properties of definite integrals.
FUN-6.A.1: In some cases, a definite integral can be evaluated by using geometry and the connection between the definite integral and area.
FUN-6.A.2: Properties of definite integrals include the integral of a constant times a function, the integral of the sum of two functions, reversal of limits of integration, and the integral of a function over adjacent intervals.
FUN-6.A.3: The definition of the definite integral may be extended to functions with removable or jump discontinuities.
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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