Analysis Assignment Example | Topics and Well Written Essays - 500 words - 3

Analysis - Assignment Example x) ≠¥ 0 over an interval a≠¤ x ≠¤b, we examine the area of this region that is said to be included in the graph of f(x) and over the interval [a, b] found on the x-axis. The area found under the region marked x = 0 and x = 1 is called the â€Å"area found under a curve†. This is an aspect that makes it related to an integral. An integral refers to associated notion of the ant derivative, a function X whose derivative is x, which is the given function. The use of integrals is a vital part in calculus and was well explained that integral includes rectangles having infinite sums and with infinitesimal width. Riemann stated that this integral basis itself on limiting procedures that appropriates a curvilinear region by approximating its area as it breaks them to thin vertical blocks (Rana, 2002). As explained by the Riemann integration, it is evident that x is a set bound by finite points sets. According to the Riemann integration theorem, the function h is defined as the indicator functions, which are equal to the figures that are on the opposite sides. This integration explains that you can use continuous functions to find and substitute the figures inside. The characteristics function definition has a formula, which gives us the opportunity to compute the value of h if we realize the distribution function Z (Taylor, 2006). Exercise 4.13 you have studied over the last few years how calculus is made rigorous with definitions (of continuity, derivative, integral, convergence, etc) and theorems. Is this necessary and/or important? Why, or why not? The use of differentiation is an aspect that is fundamental in calculus. This is based on the functions used as they are continuous. These formulas help in the derivation of the rules of Leibniz integral. The use of functions, numbers, limits, and integration is a vital aspect also in the calculations of calculus (Pfeffer, 2001). KURTZ, D. S., & SWARTZ, C. (2004). Theories of integration the integrals of Riemann,