Copyright

Ch 61: Integrals & Antiderivatives

About This Chapter

This chapter is all about the mathematic techniques and components involved with the use of integrals and antiderivatives. The lessons go over related calculations, measurements, functions, and more.

Integrals & Antiderivatives - Chapter Summary

This chapter covers mathematic principles, calculations, and methods relevant to the presence and application of integrals and antiderivatives. You'll learn about topics such as finding the arc length of a function, solving integrals using substitution, using integration by parts, as well as all of the following:

  • Indefinite integrals in relation to antiderivatives
  • Using sigma notation
  • Indefinite integrals of polynomials
  • Calculating integrals of simple shapes, trigonometric functions, and exponential functions
  • Substitution techniques for difficult integrals

Within each lesson you'll find the option of receiving the content through a video or transcript, enabling you to choose the learning style that works best for you. The timeline feature underneath the videos allows you to hop around the lesson's main points, while readers of the transcripts will find bolded words throughout, making it easy to spot key terms.

10 Lessons in Chapter 61: Integrals & Antiderivatives
Test your knowledge with a 30-question chapter practice test
Indefinite Integrals as Anti Derivatives

1. 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

2. 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.

Using Sigma Notation for the Sum of a Series

3. Using Sigma Notation for the Sum of a Series

In math, we have a notation for a lot of things. When you need to sum up a series, we also have a notation for that. You will learn about this notation, called Sigma notation, in this video lesson.

Calculating Integrals of Simple Shapes

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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!

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Other Chapters

Other chapters within the PCAT: Study Guide & Test Prep course

Support