Chapter 3
From Definite to Indefinite: The Indefinite Integral
In This Chapter
Approximating area in five different ways
Calculating sums and definite integrals
Looking at the Fundamental Theorem of Calculus (FTC)
Seeing how the indefinite integral is the inverse of the derivative
Clarifying the differences between definite and indefinite integrals
The first step to solving an area problem — that is, finding the area of a complex or unusual shape on the graph — is expressing it as a definite integral. In turn, you can evaluate a definite integral by using a formula based on the limit of a Riemann sum (as I show you in Chapter 1).
In this chapter, you get down to business calculating definite integrals. First, I show you a variety of different ways to estimate area. All these methods lead to a better understanding of the Riemann sum formula for the definite integral. Next, you use this formula to find exact areas. This rather hairy method of calculating definite integrals prompts a ...
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