Ch 30: OAE Mathematics: Area Under the Curve & Integrals

About This Chapter

The OAE Mathematics exam may ask you questions related to the area under curves and integrals. We'll help you review this concept through a series of fun and interesting video lessons.

OAE Mathematics: Area Under the Curve & Integrals - Chapter Summary

This chapter explores graphs of functions and the properties of the areas underneath the curve and integrals. We'll help you review these properties through graphs and mathematical notation. The chapter also reviews the definition of integrals and its relation to the area under a curve. At the end of the chapter, the relationship between derivatives and integrals will be reviewed. After you complete this chapter, you will have studied:

  • Riemann sums
  • Limits of Riemann sums
  • Definite integrals, their linear properties, and their relationship to Riemann sums
  • Average value theorem
  • The fundamental theorem of calculus
  • Indefinite integrals and anti-derivatives

Our video lessons are quick and convenient ways to review the important concepts on your upcoming exam. Each video lesson has a series of questions attached. These questions are modeled on the upcoming exam and can help you gain familiarity with the question types you will encounter.

Objectives of the OAE Mathematics: Area Under the Curve & Integrals Chapter

Ohio has structured its OAE mathematics exam to test information across five domains. This chapter links to the trigonometry and calculus section. There are a total of 150 multiple-choice questions on the exam and 19% of the questions come from this section. The test is only 225 minutes long and it is also computer based.

8 Lessons in Chapter 30: OAE Mathematics: 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

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Other Chapters

Other chapters within the Ohio Assessments for Educators - Mathematics (027): Practice & Study Guide course

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