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

About This Chapter

The Washington Educator Skills Test (WEST) is now the National Evaluation Series examination. Study this chapter to review the area under the curve and integrals in preparation for earning a teaching endorsement.

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

Use the video lessons in this chapter to review Riemann sums, antiderivatives and definite integrals. Reinforce what you know about left, right and middle sums as well as the zero integral property. The lessons in this chapter could help you with:

  • Finding the limits of Riemann sums and using sum notation
  • Defining integrals and indefinite integrals
  • Calculating multiple and infinite slices
  • Reviewing backward, constant and zero properties
  • Using the average value and fundamental theorems

These instructor-led video lessons contain some of the information you'll find on the WEST Math examination. Watch the lessons and submit your questions to the instructors. You'll be able to study at your own pace. Use the video tags to re-watch portions or all of the lessons, which include corresponding text transcripts. The self-assessment quizzes and practice chapter examination will measure your retention.

8 Lessons in Chapter 30: WEST 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 NES Mathematics - WEST (304): Practice & Study Guide course