Login
Copyright

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

About This Chapter

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

12 Lessons in Chapter 10: Area Under the Curve & Integrals: Calculus Lesson Plans
Summation Notation and Mathematical Series

1. Summation Notation and Mathematical Series

The capital Greek letter sigma might be most recognizable as a common symbol in a fraternity or sorority, but it's used for some pretty cool math tricks too. In this lesson, learn how to use sigma for things like determining how many seats are in Michigan Stadium.

How to Use Riemann Sums for Functions and Graphs

2. How to Use Riemann Sums for Functions and Graphs

Find out how Riemann sums can be used to calculate multiple areas efficiently. In this lesson, you'll learn how this can come in handy for irregular areas and how you can put it to use.

How to Identify and Draw Left, Right and Middle Riemann Sums

3. How to Identify and Draw Left, Right and Middle Riemann Sums

To overestimate or underestimate? In this lesson, you will draw Riemann rectangles so the right side, left side or middle of the rectangle hits the curve.

What is the Trapezoid Rule?

4. What is the Trapezoid Rule?

In this lesson, you'll move beyond simple rectangles to estimate the area under a curve. Get more sophisticated with your approximations and use trapezoids instead of those pesky rectangles.

How to Find the Limits of Riemann Sums

5. How to Find the Limits of Riemann Sums

What would happen if you could draw an infinite number of infinitesimally thin rectangles? You'd get the exact area under a curve! Define the Holy Grail of calculus, the integral, in this lesson.

Definite Integrals: Definition

6. Definite Integrals: Definition

Explore how driving backwards takes you where you've already been as we define definite integrals. This lesson will also teach you the relationship between definite integrals and Riemann sums. Then, discover how an integral changes when it is above and below the x-axis.

How to Use Riemann Sums to Calculate Integrals

7. How to Use Riemann Sums to Calculate Integrals

As a new property owner, you might relish mowing your lawn. Up and down your property you mow and measure out small sections to find the area of your property. In this lesson, you will discover what a Riemann sum approach is and how to calculate an estimated area using multiple slices.

Linear Properties of Definite Integrals

8. Linear Properties of Definite Integrals

If you're having integration problems, this lesson will relate integrals to everyday driving examples. We'll review a few linear properties of definite integrals while practicing with some problems.

Average Value Theorem

9. Average Value Theorem

If you know you've gone 120 miles in 2 hours, you're averaging 60 mph. But what if you know your velocity at every point in time and not how far you've gone? In this lesson, learn how to calculate average values using integrals.

The Fundamental Theorem of Calculus

10. The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.

Indefinite Integrals as Anti Derivatives

11. Indefinite Integrals as Anti Derivatives

What does an anti-derivative have to do with a derivative? Is a definite integral a self-confident version of an indefinite integral? Learn how to define these in this lesson.

How to Find the Arc Length of a Function

12. How to Find the Arc Length of a Function

You don't always walk in a straight line. Sometimes, you want to know the distance between two points when the path is curved. In this lesson, you'll learn about finding the length of a curve.

Earning College Credit

Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support