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The Calculus Lifesaver by Adrian Banner

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CHAPTER 17 _____________________________

The Fundamental Theorems of Calculus

Here it is: the big kahuna. I’m talking about the Fundamental Theorems of Calculus, which not only provide the key for finding definite integrals without using messy Riemann sums, but also show how differentiation and integration are connected to each other. Without further ado, here’s the roadmap for the chapter: we’ll investigate

• functions which are based on integrals of other functions;

• the First Fundamental Theorem, and the basic idea of antiderivatives;

• the Second Fundamental Theorem; and

• indefinite integrals and their properties.

After all this theoretical stuff, we’ll look at a lot of different examples in the following categories:

• problems based on ...

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