Chapter 14

Integration—Fundamentals

In Chapters 8 and 9, we met one of the main branches of calculus—differential calculus. We now introduce the other branch—integral calculus.

In the first two sections, we consider two apparently unrelated problems. We then show that the two are intimately related by the fundamental theorem of calculus, a result which links differential and integral calculus.

The first problem considered is an inverse problem. We know from Chapter 8 that, if F is differentiable, then f = F' is another function. If we are given f, can we find an F with F' = f? The function F is called an antiderivative of f. The most general antiderivative is the indefinite integral of f. Using our table of standard derivatives ‘in reverse’, ...

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