Nov 22, 2012 · Definite vs Indefinite Integrals . Calculus is an important branch of mathematics, and differentiation plays a critical role in calculus. The inverse process of the differentiation is known as integration, and the inverse is known as the integral, or simply put, the inverse of differentiation gives an integral.
Definite and Indefinite Integration has been explained here in detail. Click to learn about the concepts with their properties, problems, formulas and more. Integration means summation. Integration originated during the course of finding the area of a plane figure.When the sum of an infinite geometric series exists, we can calculate the sum. The formula for the sum of an infinite series is related to the formula for the sum of the first [latex]n[/latex] terms of a geometric series.
Properties of the Definite Integral. The properties of indefinite integrals apply to definite integrals as well. Definite integrals also have properties that relate to the limits of integration. These properties, along with the rules of integration that we examine later in this chapter, help us manipulate expressions to evaluate definite integrals. Dec 02, 2008 · Now subtract 1 and divide each term in the series by x to get: (e^x -1)/x = 1 + x/ 2! + x^2/ 3! + x^3 /4! + ... Now integrate term by term (Note: not all infinite series can be integrated term by term; however, power series can always be integrated term by term in the interval of convergence): So the integral will be: