Calculus, AP Calculus AB, AP Calculus BC, College Calculus, Calculus Honors, Area Under a Curve
This is the first lesson in a ten-lesson unit on Integration for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus.
Every lesson includes:
✎ A set of Guided Student Notes
✎ A daily homework assignment
✎ Four forms of a daily homework quiz, warm up, or exit ticket
✎ Teachers also have the benefit of a fully-editable SMART Board® Lesson
for presentation and discussion.
The SMART Board lesson can be used in many ways.
Teachers can display the presentation using the following:
* SMART Board
* Wireless Slate
* SMART Notebook for iPAD® App
* Through the SMART Notebook Express®
* Use Left, Right, and Midpoint Riemann Sums and Trapezoidal Rule to estimate area under a curve
College Board® Learning Objectives:
LO3.2B: Approximate a definite integral
LO3.2C: Calculate a definite integral using areas and properties of definite integrals
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.
The unit includes:
1) Area Under A Curve
2) Properties of Definite Integral
3) Antiderivatives & Indefinite Integration
4) Sigma Notation and Writing Area as a Limit
5) The Fundamental Theorem of Calculus
6) Mean Value Theorem for Integrals
7) Integration By Substitution
8) The Accumulation Functions
9) Integration of Transcendental Functions
10) Another Look at Particle Motion
You may also be interested in the Integration Review & Assessment Bundle.
DO YOU NEED THE FULL UNIT BUNDLE?
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