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

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### About This Chapter

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

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### Other Chapters

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

- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Reasoning
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Systems of Equations
- NES Math: Complex Numbers
- NES Math: Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Rate of Change
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Properties of Triangles
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Trigonometric Identities
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation