Ch 15: Integration

About This Chapter

Boost your confidence ahead of an upcoming exam by reviewing the helpful lessons on math integration provided in this chapter. These self-paced video and text lessons cover all the topics you'll need to know on test day in order to get the highest grade possible.

Integration - Chapter Summary

In this engaging chapter, you'll learn all about integration in mathematics, including the definition of definite integrals, using anti-derivatives to calculate the indefinite integrals of polynomials and the trapezoid rule. Our short, user-friendly lessons also cover the formula associated with Simpson's Rule and the use of substitution to solve integrals. Other topics include integration by parts and finding simple areas with integration and root finding. Once you complete this chapter, you should be ready to:

  • Integrate functions with partial fractions
  • Give an example of partial fraction decomposition
  • Complete the square to integrate functions
  • Use integration to find volumes of revolution
  • Solve practice problems involving the volume of a solid of revolution

You can work at your own pace as you access these learning tools on your mobile phone, tablet or computer. All of our lessons are followed by a multiple-choice quiz so you can test your understanding of the subjects. Feel free to watch the video lessons as many times as you need to in order to master the information, or use the video tabs feature to skip directly to a specific section.

11 Lessons in Chapter 15: Integration
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.

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.

What is the Trapezoid Rule?

3. What is the Trapezoid Rule?

In this lesson, you'll move beyond simple rectangles to estimate the area under a curve. Get more sophisticated with your approximations and use trapezoids instead of those pesky rectangles.

What is Simpson's Rule? - Example & Formula

4. What is Simpson's Rule? - Example & Formula

In this lesson, you'll learn how to approximate the integration of a function using a numerical method called Simpson's Rule. This method is particularly useful when integration is difficult or even impossible to do using standard techniques.

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.

Using Integration By Parts

6. 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!

How to Find Simple Areas With Root Finding and Integration

7. How to Find Simple Areas With Root Finding and Integration

Combine your calculus tools in this lesson! Find the area enclosed by multiple arbitrary functions by first finding the root of an equation and then integrating over the resulting range.

How to Integrate Functions With Partial Fractions

8. 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!

Partial Fraction Decomposition: Rules & Examples

9. Partial Fraction Decomposition: Rules & Examples

What if you had a way to expand certain large math expressions into smaller pieces? This would make some calculus integrals easier to solve. In this lesson, we explore such a method: partial fraction decomposition.

How to Integrate Functions by Completing the Square

10. How to Integrate Functions by Completing the Square

We want to integrate a rational function that includes a polynomial by expressing the polynomial as the sum or difference of two squares so that we can apply a substitution (trigonometric or logarithmic).

How to Find Volumes of Revolution With Integration

11. 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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