# Ch 31: NES Math: Integration Techniques

### About This Chapter

## NES Math: Integration Techniques - Chapter Summary

Use the short video lessons, quizzes and other study aids in this chapter to review information about integrals, including how to calculate and solve problems. As you study for the NES Math test, you can renew your understanding of topics such as:

- Integral calculations of simple shapes
- How to calculate indefinite integrals of polynomials
- How to solve integrals with substitution
- Ways to use integration by parts

Humor, animation and the liberal use of real-world examples make these lessons lively and informative, and you can study via computer, tablet or smartphone from anywhere there's Internet access. The short lesson quizzes and a comprehensive chapter exam allow you to assess your knowledge and see where you need extra study. A clickable Timeline makes it quick work to return to key points in the lesson for review.

### NES Math: Integration Techniques Objectives

In five states, the NES Math test is one of the requirements for certification to teach math at the secondary level. All questions on the test are multiple-choice, and the test is computer-delivered. The quizzes in this study guide are in the same format, so the test's questions will be familiar.

The questions on the NES Math test are divided into five content domains, and questions on integration techniques are in the Trigonometry and Calculus content domain. This content domain accounts for 19% of the test's total score.

### 1. Calculating Integrals of Simple Shapes

So you can write something called an integral with a weird squiggly line. Now what? In this lesson, calculate first integrals using your knowledge of nothing but geometry.

### 2. Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

If you throw a ball in the air, the path that it takes is a polynomial. In this lesson, learn how to integrate these fantastic functions by putting together your knowledge of the fundamental theorem of calculus and your ability to differentiate polynomial functions.

### 3. How to Solve Integrals Using Substitution

Some integrals are as easy as riding a bike. But more often, integrals can look like deformed bikes from Mars in the year 3000. In this lesson, you will learn how to transform these scary-looking integrals into simpler ones that really are as easy as riding a bike.

### 4. Using Integration By Parts

Your mother may have warned you not to bite off more than you can chew. The same thing is true with integration. In this lesson, learn how integration by parts can help you split a big interval into bite-sized pieces!

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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: 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
- NES Mathematics Flashcards