About This Chapter
Who's It For:
Anyone who needs help learning or mastering integrals material will benefit from the lessons in this chapter. There is no faster or easier way to learn integrals in business calculus. Among those who would benefit are:
- Students who have fallen behind in understanding integrals in business calculus
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning business (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about integrals in business calculus
- Students who struggle to understand their teachers
- Students who attend schools without extra business learning resources
How It Works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Integrals in Business Calculus 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 Integrals in Business Calculus chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question about integrals in business calculus. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students Will Review:
This chapter helps students review the concepts in an integrals unit of a standard business calculus course. Topics covered include:
- Indefinite and definite integrals
- Fundamental Theorem of Calculus
- Solving integrals using substitution including techniques for difficult integrals
- Integration by parts
1. 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.
2. 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.
3. 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.
4. 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.
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.
6. 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.
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!
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Other chapters within the Business Calculus: Help & Review course
- Functions for Business Calculus
- Working with Limits in Business Calculus
- Derivatives & Differentiation in Business Calculus
- Calculating & Graphing Derivatives in Business Calculus
- Derivatives of Functions in Business Calculus
- Optimization in Business Calculus
- Logarithms in Business Calculus
- Growth Models in Business Calculus
- Multi-Variable Calculus