About This Chapter
Integration in Calculus - Chapter Summary
Discover or get reacquainted with the basics of integration in calculus with help from short videos and other helpful study resources. Watch lessons at home or anywhere you can access the Internet to ensure you understand anti-derivatives, definite integrals, how to calculate various types of integrals and more. Completing this chapter will enable you to:
- Define definite integrals, and evaluate them using the fundamental theorem
- Calculate indefinite integrals of polynomials
- Find integrals of trigonometric and exponential functions
- Use substitution to solve integrals
- Split big intervals using integration by parts
- Integrate fractions using the partial fractions technique
Boost your knowledge of integration in calculus by reviewing the lessons as short videos or full transcripts. It's your choice! Videos keep you engaged with entertaining visual effects, and transcripts allow you to print the materials or take notes right on your computer. If you want to clarify a topic after reviewing a lesson, feel free to use the Ask Our Experts feature to submit your question. Confirm that you fully understand integration in calculus by taking this chapter's self-assessment quizzes and practice exam.
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.
2. Evaluating Definite Integrals Using the Fundamental Theorem
The fundamental theorem of calculus makes finding your definite integral almost a piece of cake. See how the definite integral becomes a subtraction problem after applying the fundamental theorem of calculus.
3. 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.
4. 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.
5. 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!
6. 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.
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!
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!
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