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

About This Chapter

Use this chapter's video lessons to catch up on area under the curve and integrals as you study for relevant test questions on the GACE Math exam. Lesson topics include Riemann sums, the average value theorem and the fundamental theorem of calculus.

GACE Math: Area Under the Curve and Integrals - Chapter Summary

The lessons in this chapter strengthen your knowledge of area under the curve and integrals and provide opportunities to solve practice problems. Review Riemann sums and analyze the applications of various mathematical theories. These lessons to expand your ability to:

  • Use Riemann sums to calculate areas and integrals
  • Calculate the limits of Riemann sums
  • Explain the difference between definite integrals and Riemann sums
  • Describe the properties of definite integrals
  • Define and apply the average value theorem
  • Explain and apply the fundamental theorem of calculus
  • Define indefinite integrals

Delivered by credentialed instructors, these video lessons help to solidify your knowledge of area under the curve and integrals. Watch the lessons and learn at your own pace. Use the video tags to review certain parts of the video, if needed. Written transcripts mirror the information in the videos. You can test your understanding by taking the self-assessment quizzes.

GACE Math: Area Under the Curve and Integrals - Chapter Objectives

When taking the GACE Math examination, you'll need to display your familiarity with a wide range of advanced mathematics principles, including the area under the curve and integrals concepts that you studied in this chapter. Consisting of two subtests, the tests is delivered via computer. You'll answer 45 multiple-choice questions on each part of the examination.

8 Lessons in Chapter 30: GACE 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.
Not Taken

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Other Chapters

Other chapters within the GACE Mathematics (522): Practice & Study Guide course

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