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Ch 30: TExMaT Master Mathematics Teacher 8-12: Area Under the Curve & Integrals

About This Chapter

Strengthen your capacity to understand and teach topics pertaining to area under the curve and integrals. Watch the online video lessons in this chapter prior to answering pertinent questions on the TExMaT Master Mathematics Teacher 8-12 examination.

TExMaT Master Mathematics Teacher 8-12: Area Under the Curve and Integrals - Chapter Summary

Through step-by-step examples and illustrations, this chapter's video lessons will attempt to expand your ability to find areas under the curve and to calculate integrals. Discover how much you recall about topics such as Riemann sums, the fundamental theorem and the average value theorem as you get set to pass the TExMaT Master Mathematics Teacher 8-12 examination. This chapter could assist you with:

  • Calculating integrals with Riemann sums and finding the limits of Riemann sums
  • Defining definite integrals and understanding linear properties
  • Using the average value theorem and the fundamental theorem of calculus
  • Calculating indefinite integrals

Utilize the educational video lessons to revisit these mathematics concepts. Study at a pace that is comfortable for you and ask questions if necessary. Evaluate your readiness to take the TExMaT Master Mathematics Teacher 8-12 examination by completing the lesson quizzes and the practice chapter examination.

TExMaT Master Mathematics Teacher 8-12: Area Under the Curve and Integrals Chapter Objectives

You could find questions on area under the curve and integrals when you reach the Precalculus and Calculus section of the TExMaT Master Mathematics Teacher 8-12 examination. This is where you'll earn 16% of the whole examination score. Demonstrate the mathematics expertise you gained from your prior education as well as from your review of this chapter's material. You'll have five hours to answer 90 multiple-choice questions on the paper-administered test. You must also complete one case study assignment during that time frame.

8 Lessons in Chapter 30: TExMaT Master Mathematics Teacher 8-12: 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 TExMaT Master Mathematics Teacher 8-12 (089): Practice & Study Guide course

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