Ch 43: FTCE Math: Integration & Integration Techniques

About This Chapter

Let us help you prepare for the FTCE Math exam. We have put together a chapter that will help you review topics that deal with integration and integration techniques.

FTCE Math: Integration & Integration Techniques - Chapter Summary

This chapter was created so that you can quickly review integration topics that you might see on the FTCE Math exam. Some of these include:

  • Definite integrals
  • Fundamental Theorem of Calculus
  • Finding arc length of a function
  • Calculating the integrals of similar shapes and polynomials
  • Anti-derivatives
  • Calculating integrals of exponential functions and trigonometric functions
  • Integration by parts
  • Solving improper integrals
  • Using substitution to solve integrals

In order to quickly better your skills at solving integration problems, which will be on the test, you can go through our video lessons. These lessons are interactive, so you can learn in a fun manner and easily retain information. To make sure you are picking up the right strategies to work with integrals, you can take a quiz at the end of every lesson. The quizzes will help you see if you are ready for the real exam or not.

15 Lessons in Chapter 43: FTCE Math: Integration & Integration Techniques
Test your knowledge with a 30-question chapter practice test
Definite Integrals: Definition

1. 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.

Linear Properties of Definite Integrals

2. 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.

The Fundamental Theorem of Calculus

3. 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.

Indefinite Integrals as Anti Derivatives

4. 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.

How to Find the Arc Length of a Function

5. How to Find the Arc Length of a Function

You don't always walk in a straight line. Sometimes, you want to know the distance between two points when the path is curved. In this lesson, you'll learn about finding the length of a curve.

Calculating Integrals of Simple Shapes

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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!

Understanding Trigonometric Substitution

13. 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

14. 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

15. 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.

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 FTCE Mathematics 6-12 (026): Practice & Study Guide course

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