# Ch 32: NES Math: Applications of Integration

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### About This Chapter

## NES Math: Applications of Integration - Chapter Summary

Brush up on integrals and the ways in which they are used by watching our short video lessons. The material in this chapter of our study guide can help you handle NES Math test questions on topics such as:

- Dynamic motion and integration
- The use of single integrals to calculate volumes
- How to use integration to find volumes of revolution

Our instructors have developed entertaining lessons that make their points with examples and humor. You can test your knowledge with short quizzes and a chapter exam. A clickable Timeline lets you quickly jump back to the lesson to review key passages without having to re-watch the entire video. You can keep up with your progress through our personalized Dashboard, which may even offer some suggestions about other courses that could help you.

### NES Math: Applications of Integration Chapter Objectives

Several states require passing the NES Math test as a condition for certification to teach math at the secondary level. The test consists entirely of multiple-choice questions and is administered by computer. Our lesson quizzes and chapter exam also are computer-based multiple-choice tests, so taking them will give you practice in answering questions like those you'll face on the NES test in addition to helping you gauge your learning.

The NES Math test is divided into five sections, called content domains. Questions related to the applications of integration will be asked during the exam's Trigonometry and Calculus content domain, which makes up 19% of the test's score.

### 1. Integration and Dynamic Motion

This lesson uses driving to demonstrate how graphing can help you use calculus to figure out how fast you were going at a given time. Using this lesson, you can learn how to integrate your velocity to find your position.

### 2. How to Calculate Volumes Using Single Integrals

Ever wonder where the equation for the volume of a cone comes from? Or the equation for the volume of a sphere? In this lesson, learn how to use a slicing technique to find the volume of a region by solving a single integral.

### 3. How to Find Volumes of Revolution With Integration

Some shapes look the same as you rotate them, like the body of a football. In this lesson, learn how to find the volumes of shapes that have symmetry around an axis using the volume of revolution integration technique.

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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: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- 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