The last section of this chapter deals with definite integrals. The concept of integral plays a fundamental role in calculus and applied mathematics and, as we shall see, it is in a sense the opposite operation with respect to taking derivatives. In the book, we use definite integrals essentially to deal with continuous random variables in probability theory.26 In that context, it is sufficient to understand definite integrals as a way to compute an area, which has the meaning of a probability. Hence, we introduce the definite integral as the area below the graph of a function. We also try to get some business motivation for introducing integrals in models where time is continuous. What we will not do is lay down rigorous foundations for the concept, which would be outside the scope of the book, or developing sophisticated technical skills and tricks to find integrals in intricate cases.
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