Ch 49: CEOE Advanced Math: Integration Techniques

About This Chapter

This chapter on integration techniques will provide you with a thorough and easy-to-follow review of everything you'll want to know on this subject going into the CEOE Advanced Mathematics exam.

CEOE Advanced Math: Integration Techniques - Chapter Summary

This chapter goes over the principles and methods of integration within mathematics, hitting on all the related topics you may encounter on the test. By the end of this chapter, you'll be better prepared to answer questions concerning the following:

  • Calculating integrals of simple shapes, trigonometric functions, and exponential functions
  • Anti-derivatives and calculating indefinite integrals of polynomials
  • Solving integrals using substitution
  • Techniques for substituting difficult integrals
  • Integration by parts
  • Partial fractions and integrating functions with them
  • Trigonometric substitution and using it to solve integrals
  • Solving improper integrals
  • Finding volumes of revolution with integration

Each lesson includes both a video and transcript of the content, allowing you to choose the learning method that fits you best. You'll find the material simple to navigate, with the timeline feature enabling you to jump straight to key points within the video and the transcript filled with important terms highlighted in bold.

CEOE Advanced Math: Integration Techniques Chapter Objectives

The CEOE Advanced Mathematics exam is a core component of the teacher certification process in the state of Oklahoma for those seeking licensure as an advanced math instructor. The exam is composed of 80 multiple-choice questions spread through five subareas and one constructed-response (written) assignment that will pertain to the relations, functions, and algebra subarea.

The lessons in this chapter are applicable to the trigonometry and calculus subarea of the exam, which contains questions about the principles and techniques of integral calculus. As a whole, this subarea makes up 23% of the exam's content.

13 Lessons in Chapter 49: CEOE Advanced Math: Integration Techniques
Test your knowledge with a 30-question chapter practice test
Calculating Integrals of Simple Shapes

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.

Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

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.

How to Calculate Integrals of Trigonometric Functions

3. How to Calculate Integrals of Trigonometric Functions

Ever feel like you are going around in circles? Like, periodically you have your ups and downs? Well, sines and cosines go up and down regularly too. In this lesson, learn how to integrate these circular functions.

How to Calculate Integrals of Exponential Functions

4. How to Calculate Integrals of Exponential Functions

Exponential functions are so predictable. It doesn't matter how many times you differentiate e^x, it always stays the same. In this lesson, learn what this means for finding the integrals of such boring functions!

How to Solve Integrals Using Substitution

5. 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.

Substitution Techniques for Difficult Integrals

6. Substitution Techniques for Difficult Integrals

Up, down. East, West. Opposites are everywhere. In this lesson, learn how you can think of substitution for integration as the opposite of the chain rule of differentiation.

Using Integration By Parts

7. 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!

Partial Fractions: How to Factorize Fractions with Quadratic Denominators

8. Partial Fractions: How to Factorize Fractions with Quadratic Denominators

Adding fractions with different denominators is something you probably learned how to do in algebra. In this lesson, learn how to do the opposite: take a complicated fraction and turn it into two simpler ones.

How to Integrate Functions With Partial Fractions

9. How to Integrate Functions With Partial Fractions

In this lesson, learn how to integrate complicated fractions by using the partial fractions technique. That is, you will turn a complicated fraction into something a bit easier to integrate by finding partial fractions!

Understanding Trigonometric Substitution

10. Understanding Trigonometric Substitution

Sometimes a simple substitution can make life a lot easier. Imagine how nice it would be if you could replace your federal tax form with a 'Hello, my name is...' name badge! In this lesson, we review how you can use trigonometry to make substitutions to simplify integrals.

How to Use Trigonometric Substitution to Solve Integrals

11. How to Use Trigonometric Substitution to Solve Integrals

In this lesson, we use each of the common integration techniques to solve different integrals. It's not always obvious which technique will be the easiest, so being familiar with an arsenal of methods might save you a lot of work!

How to Solve Improper Integrals

12. How to Solve Improper Integrals

What does it mean when an integral has limits at infinity? These integrals are 'improper!' In this lesson, learn how to treat infinity as we study the so-called improper integrals.

How to Find Volumes of Revolution With Integration

13. 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.

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.
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Other Chapters

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

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