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Ch 11: Integration and Integration Techniques: Help and Review

About This Chapter

The Integration and Integration Techniques chapter of this College Calculus Help and Review course is the simplest way to master integration and integration techniques. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of integration and integration techniques.

Who's it for?

Anyone who needs help understanding material from college calculus will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:

  • Have fallen behind in understanding integration or working with integration techniques.
  • Need an efficient way to learn about integration and integration techniques.
  • Learn best with engaging auditory and visual tools.
  • Struggle with learning disabilities or learning differences, including autism and ADHD.
  • Experience difficulty understanding your teachers.
  • Missed class time and need to catch up.
  • Can't access extra math learning resources at school.

How it works:

  • Start at the beginning, or identify the topics that you need help with.
  • Watch and learn from fun videos, reviewing as needed.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Submit questions to one of our instructors for personalized support if you need extra help.
  • Verify you're ready by completing the Integration and Integration Techniques chapter exam.

Why it works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the Integration and Integration Techniques chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students will review:

In this chapter, you'll learn the answer to questions including:

  • How do I calculate integrals of simple shapes?
  • What do I do to calculate integrals of polynomials?
  • How do I calculate integrals of exponential or trigonometric functions?
  • How do I use substitution to simplify complex integrals?
  • What steps do I follow when factoring fractions with quadratic denominators?
  • What is trigonometric substitution, and how is it used to calculate improper integrals?

16 Lessons in Chapter 11: Integration and Integration Techniques: Help and Review
Test your knowledge with a 30-question chapter practice test
Calculating Integrals of Simple Shapes

1. Calculating Integrals of Simple Shapes

Explore descriptions of how to calculate the definite integral of simple shapes through geometry. Learn how to calculate the integral of a simple shape, such as a rectangle or a trapezoid, find the area under the curve, and solve for the area.

Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

2. Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

The indefinite integral of ''f(x)dx'' can be written as the anti-derivative of ''f(x)'' plus some integration constant. Explore more about anti-derivatives and calculating indefinite integrals of polynomials with examples included in this lesson.

How to Calculate Integrals of Trigonometric Functions

3. How to Calculate Integrals of Trigonometric Functions

Discover the two main integrals of trigonometric functions that are the most important to understand. Review how integrals are calculated and the integrals of sine and cosine and study examples of calculating these integrals.

How to Calculate Integrals of Exponential Functions

4. How to Calculate Integrals of Exponential Functions

Taking the derivative of the function e^x results in e^x, while taking the indefinite integral of e^x dx equals e^x + C. Review examples of how to calculate integrals of exponential functions.

How to Solve Integrals Using Substitution

5. How to Solve Integrals Using Substitution

Consider how to solve integrals using substitution, which is a result of a tool called the chain rule. Review the chain rule and its uses in solving substitution, find examples of substitution, and discover how to check the answer to a problem.

Substitution Techniques for Difficult Integrals

6. Substitution Techniques for Difficult Integrals

Most integrals can be solved by looking them up in a table or by replacing part of the function with ''u'' substitution. Learn more about solving difficult integrals using substitution techniques.

Using Integration By Parts

7. Using Integration By Parts

Integration by parts takes the integral udv and separates it into uv and another integral that is easier to solve. Discover more about the mathematical concept and how it is similar to completing a jigsaw puzzle.

Partial Fractions: How to Factorize Fractions with Quadratic Denominators

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

Solving equations with partial fractions is made easier by factoring and determining what the undetermined coefficients A and B are. Learn how to factorize fractions that have quadratic denominators with problem examples.

How to Integrate Functions With Partial Fractions

9. How to Integrate Functions With Partial Fractions

Discover how to integrate complex functions with partial fractions. Learn about partial fractions and when to use them, when to use ~'u~' substitutions, and find examples of how to integrate functions using these techniques.

Understanding Trigonometric Substitution

10. Understanding Trigonometric Substitution

Trigonometric substitution uses substitutions based on trigonometric identities. Gain an enhanced understanding of using trigonometric substitutions to simplify integrals by reviewing a series of examples.

How to Use Trigonometric Substitution to Solve Integrals

11. How to Use Trigonometric Substitution to Solve Integrals

Solving problems of integration may involve memorizing certain integrals, such as sin(x) and 1/x, or may involve other tools like Riemann Sums. Explore more about solving integrals with trigonometric substitution.

How to Solve Improper Integrals

12. How to Solve Improper Integrals

Improper integrals have either a positive or negative infinity. Explore how to solve them by splitting up the integrals and replacing infinity with a variable.

Initial Value in Calculus: Definition, Method & Example

13. Initial Value in Calculus: Definition, Method & Example

In this lesson, you'lll learn about how the initial value of calculus is related to the integration process. You will see how crucial having an initial condition is and how useful it is in solving your problems.

Midpoint Rule: Formula & Example

14. Midpoint Rule: Formula & Example

Finding an estimate for the area under a curve is a task well-suited to the midpoint rule. In this lesson we use an example to show the general idea of this formula and how to use it.

How to Integrate xe^x: Steps & Tutorial

15. How to Integrate xe^x: Steps & Tutorial

In this lesson, we use the product rule and integration by parts to find the integral of xe^x. The natural extension of integration by parts leads to a reduction formula which elegantly extends the integration results.

How to Integrate sec(5x): Steps & Tutorial

16. How to Integrate sec(5x): Steps & Tutorial

In this lesson you will learn how to integrate sec 5x using two different methods. After showing the results are equivalent, we will verify the solution and use it to find the area under the curve of sec 5x over a finite interval.

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

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