Calculus Essentials For Dummies

Chapter 9

Integration: Backwards Differentiation

IN THIS CHAPTER

Antidifferentiating — putting ’er in reverse

Using the area function

Getting familiar with the Fundamental Theorem of Calculus

Chapter 8 shows you the hard way to calculate the area under a curve using the formal definition of integration — the limit of a Riemann sum. In this chapter, I do it the easy way, taking advantage of one of the most important discoveries in mathematics — that integration is just differentiation in reverse.

Antidifferentiation: Reverse Differentiation

Antidifferentiation is just differentiation backwards. The derivative of sin x is cos x, so the antiderivative of cos x is sin x; the derivative of is , so the antiderivative of is — you just go backwards … with one twist: The derivative of is also ...