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Calculus: Concepts and Methods by Joan Davies, Ken Binmore

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Ten

Sums and integrals

This chapter is chiefly about integrating real valued functions of one real variable. Because an integral is a generalisation of the idea of a sum, it is also convenient to include some discussion of summation in this chapter. It is assumed that readers have some previous knowledge of these subjects. In particular, §10.2–§10.9 inclusive consist of an accelerated account of elementary integration theory which a newcomer to the topic would find difficult to assimilate adequately unless they had an unusual aptitude for mathematics. However, experience shows that students are often very rusty on the techniques of integration ...

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