Methods of Integration

Michael Green

5 min read

Next Topic - Selecting Techniques for Integration

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Study Guide Overview

This study guide covers polynomial long division to simplify rational functions for integration. Key steps include identifying the dividend and divisor, dividing leading terms, multiplying, and subtracting. It includes a worked example, exam tips, and practice questions. The guide also defines terms like remainder and indefinite integral.

#Integration Using Long Division

Key Concept

#Introduction to Polynomial Long Division

Polynomial long division is a method used to simplify rational functions, making them easier to integrate. For example, consider the rational function:

$\frac{x^3 + 6x^2 - 9x - 11}{x-2}$

Using polynomial long division, we can rewrite this function in a form that is easier to integrate.

Key Concept

#Steps for Polynomial Long Division

#Step 1: Setup

Identify the dividend (the polynomial you are dividing) and the divisor (the polynomial you are dividing by).

For example:

Dividend: $x^3 + 6x^2 - 9x - 11$
Divisor: $x - 2$

#Step 2: Divi...

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Previous Topic - Integration Using Completing the Square Next Topic - Selecting Techniques for Integration

Methods of Integration

Michael Green

5 min read

Next Topic - Selecting Techniques for Integration

Listen to this study note

Study Guide Overview

#Integration Using Long Division

#Table of Contents

Introduction to Polynomial Long Division
Steps for Polynomial Long Division
Worked Example
Exam Tips
Practice Questions
Glossary
Summary and Key Takeaways

Key Concept

#Introduction to Polynomial Long Division

Polynomial long division is a method used to simplify rational functions, making them easier to integrate. For example, consider the rational function:

$\frac{x^3 + 6x^2 - 9x - 11}{x-2}$

Using polynomial long division, we can rewrite this function in a form that is easier to integrate.

Key Concept

#Steps for Polynomial Long Division

#Step 1: Setup

Identify the dividend (the polynomial you are dividing) and the divisor (the polynomial you are dividing by).

For example:

Dividend: $x^3 + 6x^2 - 9x - 11$
Divisor: $x - 2$

#Step 2: Divi...

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Give us your feedback and let us know how we can improve

Previous Topic - Integration Using Completing the Square Next Topic - Selecting Techniques for Integration