# 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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