Chapter 15

Integration: It’s Backwards Differentiation

In This Chapter

arrow Using the area function

arrow Getting familiar with the fundamental theorem of calculus

arrow Finding antiderivatives

arrow 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… .


The derivative of sinx is cosx, so the antiderivative of cosx is sinx; the derivative of 9781118791295-eq15001.eps is 9781118791295-eq15002.eps, so the antiderivative of is — you ...

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