Ch 30: ORELA Math: Area Under the Curve & Integrals

About This Chapter

These quick, appealing videos make it easy to review the integrals and area below the curve concepts educators are expected to have mastered for the ORELA Math certification assessment. Our instructors are available to offer guidance and support- reach out to them any time you need assistance.

ORELA Math: Area Under the Curve & Integrals - Chapter Summary

The ORELA Math assessment will likely include the area under the curve and integrals topics covered by the quick videos and multiple-choice quizzes in this chapter. Lesson topics include:

  • Using Riemann sums for graphs and functions
  • Calculating limits of Riemann sums
  • Using Riemann sums to calculate integrals
  • Definite and indefinite integrals
  • Average value theorem and the fundamental theorem of calculus

If, after watching a video, you still feel uncomfortable with the concepts, consult the lesson transcripts for further review. If something doesn't make sense or you get hung up on a quiz question, let our instructors know you need guidance.

8 Lessons in Chapter 30: ORELA Math: Area Under the Curve & Integrals
Test your knowledge with a 30-question chapter practice test
How to Use Riemann Sums for Functions and Graphs

1. 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 Find the Limits of Riemann Sums

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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.

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 200 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.

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.

Other Chapters

Other chapters within the ORELA Mathematics: Practice & Study Guide course

Support