April 2023
Beginner to intermediate
656 pages
17h 28m
English
Content preview from Calculus All-in-One For Dummies (+ Chapter Quizzes Online)
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Chapter 15
Integration: It’s Backwards Differentiation
IN THIS CHAPTER
Using the area function
Getting familiar with the Fundamental Theorem of Calculus
Finding antiderivatives
Figuring exact areas the easy way
Chapter 14 shows you the hard way to calculate the area under a function using the formal definition of integration — the limit of a Riemann sum. In this chapter, I calculate areas the easy way, taking advantage of one of the most important and amazing discoveries in mathematics — that integration (finding areas) is just differentiation in reverse. That reverse process was a great discovery, and it’s based on some difficult ideas, but before we get to that, let’s talk about a related, straightforward reverse process, namely …
Antidifferentiation
The derivative of 
is 
, so the antiderivative of is ; the derivative of is , so the antiderivative of is — you just go backwards. ...
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