Applications of Definite Integrals pdf


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Applications of Definite Integrals pdf

Applications of Definite Integrals pdf

Overview : We saw that a continuous function over a closed interval has a definite integral, which is the limit of Riemann sum approximations for the function. Wefound a way to evaluate definite integrals using the Fundamental Theorem of Calculus. We saw that the area under a curve and the area between two curves could be defined and computed as definite integrals. In this chapter we will see some of the many additional applications of definite integrals. We will use the definite integral to define and find volumes, lengths of plane curves, and areas of surfaces of revolution. We will see how integrals are used to solve physical problems involving the work done by a force, and how they give the location of an object’s center of mass. The integral arises in these and other applications in which we can approximate a desired quantity by Riemann sums. The limit of those Riemann sums, which is the quantity we seek, is given by a definite integral.

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