Ch 48: CEOE Advanced Math: Area Under the Curve & Integrals

About This Chapter

Take a closer look at area under the curve and integrals by exploring the short video lessons in this chapter. Self-assessment quizzes can test your knowledge of the subject area as you study for the CEOE Advanced Math assessment in Oklahoma.

CEOE Advanced Math: Area Under the Curve & Integrals - Chapter Summary

Use the lessons in this chapter to boost your confidence while preparing to take the CEOE Advanced Math assessment. Watching the videos will ensure you're able to do the following:

  • Explain how to use Reimann sums for functions and graphs
  • Identify and draw left, right and middle Riemann sums
  • Define the trapezoid rule, and find the limits of Riemann sums
  • Share the meaning of definite integrals, and use Reimann sums to calculate integrals
  • Describe linear properties of definite integrals
  • Discuss average value theorem and indefinite integrals as anti derivatives
  • Find the arc length of a function

Take advantage of the flexibility this chapter offers by reviewing the lessons in any sequence you desire and watching them as often as you deem necessary. You can also use timelines with video tags to identify and jump to key topics within the video lessons without watching them in their entirety.

CEOE Advanced Math: Area Under the Curve & Integrals Chapter Objectives

Educators take the CEOE Advanced Math assessment to secure the certification required to teach this subject in Oklahoma classrooms. The computer-based test consists of 80 selected-response questions and 1 constructed-response assignment that are broken into five subareas. Lessons in this chapter cover topics found in the trigonometry and calculus subarea, which constitutes about 23% of the total test.

In addition to reviewing the lessons in this chapter, you can brush up on your knowledge of area under the curve and integrals by taking self-assessment quizzes and a chapter exam. Any questions you have about lesson topics can be submitted to our experts. Taking these steps can improve your chances of passing the exam with a minimum score of 240.

10 Lessons in Chapter 48: CEOE Advanced 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 Identify and Draw Left, Right and Middle Riemann Sums

2. 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?

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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.

Indefinite Integrals as Anti Derivatives

9. 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

10. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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