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 ...