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

About This Chapter

Use our lessons to refresh your understanding of Riemann sums, integrals and average value theorem in preparation for the NES Math test. These videos, quizzes, question sheets and other study tools offer what you need for test success.

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

Use these lessons to renew your knowledge of Riemann sums, average value theorem and indefinite integrals as you study for the NES Math exam. Our videos and quizzes examine the following:

  • Using Riemann sums for functions and graphs
  • Finding the limits of Riemann sums
  • Definite integrals
  • Calculating integrals with Riemann sums
  • Linear properties of definite integrals
  • Average value theorem
  • The fundamental theorem
  • Anti derivatives

Our instructors understand what's required for success on the NES Math test, and they keep your interest with lively lessons filled with examples and humor. You can assess your review through lesson quizzes and a chapter exam, and, if you have questions, contact the instructor through our ask-an-expert message board. Other study aids that may be useful include printable sheets of quiz questions, a text transcript of the lesson and a personalized Dashboard that lets you track your progress.

NES Math: Area Under the Curve & Integrals Chapter Objectives

Several states make in mandatory to pass the NES Math test in order to obtain certification to teach mathematics at the secondary level. Test questions are divided into five content domains. The questions on the material in the Area Under the Curve and Integrals are in the Trigonometry and Calculus content domain, which makes up 19% of the test.

The NES Math test is administered by computer. It contains 150 multiple-choice questions which require you to select the right answer from several choices. Our lesson quizzes and the chapter exam are also computer-delivered, multiple-choice tests, so taking them will familiarize you with answering questions in this format.

8 Lessons in Chapter 30: NES 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.
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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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Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course