# Ch 10: Area Under the Curve & Integrals: Calculus Lesson Plans

The Area Under the Curve and Integrals chapter of this course is designed to help you plan and teach the students in your classroom about terms such as average value theorem, definite integrals and the Trapezoid Rule. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

## Weekly Syllabus

Below is a sample breakdown of the Area Under the Curve and Integrals chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day Topics Key Terms and Concepts Covered
Monday Summation Notation and Mathematical Series;
How to Use Riemann Sums for Functions and Graphs;
How to Identify and Draw Left, Right and Middle Riemann Sums
The use of sigma notation;
The process of using sum notation;
The process of constructing Riemann rectangles
Tuesday What is the Trapezoid Rule?;
How to Find the Limits of Riemann Sums;
Definite Integrals: Definition
Estimating area with trapezoids;
An outline of this process;
Examples of definite integrals
Wednesday How to Use Riemann Sums to Calculate Integrals;
Linear Properties of Definite Integrals
The process of calculating area;
An explanation of the zero integral property and the backward property
Thursday Average Value Theorem;
The Fundamental Theorem of Calculus
The process of finding an average value;
An explanation of this theorem
Friday Indefinite Integrals as Anti Derivatives;
How to Find the Arc Length of a Function
Using the fundamental theorem;
Finding distance with the Pythagorean theorem

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

### Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.