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6 Numerical Integration

D. Levy6 Numerical Basic ConceptsIn this chapter we are going to explore various ways for approximating the integral of afunction over a given domain. There are various reasons as of why such approximationscan be useful. First, not every function can be analytically integrated. Second, even if aclosed Integration formula exists, it might still not be the most efficient way of calculatingthe integral. In addition, it can happen that we need to integrate an unknown function,in which only some samples of the function are order to gain some insight on Numerical Integration , it is natural to review Rie-mann Integration , a framework that can be viewed as an approach for approximat-ing integrals.

6.1 Basic Concepts D. Levy For the purpose of the present discussion we can think of the upper and lower Dar-boux sums (6.1), (6.2), as two approximations of the integral (assuming that the …

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