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

About This Chapter

A NES Mathematics exam has replaced the NMTA Mathematics test for certifying math teachers in the state of New Mexico. In preparation for related questions on this exam, complete the activities of this chapter to review the steps used when calculating the area under a curve and working with integrals.

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

As part of your review for the NES Mathematics exam, use this chapter to improve your abilities working with integrals and finding the areas under a curve in calculus. After completing these chapters, you should be able to answer test questions related to:

  • Using Riemann sums and finding the limits of Riemann sums
  • Calculating integrals with Riemann sums
  • Linear properties of definite integrals
  • The average value and fundamental theorems of calculus
  • Indefinite integrals

Reinforce your retention of the information presented in these lesson videos by completing lesson quizzes. If you think you would benefit from an alternative way of reviewing the material, try reading over the lesson transcripts which offer easy to read outlines of the lessons.

NMTA Math: Area Under the Curve & Integrals Objectives

Educators in the state of New Mexico take the NES Mathematics exam to demonstrate their mathematical abilities before earning state certification. This computer-based exam is a series of 150 multiple-choice questions, and 19% of the questions are part of the trigonometry and calculus domain. Prepare for some of these questions to ask you to work with integrals by improving your abilities finding the area under a curve with the activities of this chapter.

8 Lessons in Chapter 30: NMTA 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

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Other Chapters

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

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