Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

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. ...