tailieunhanh - Ebook Fundamentals of calculus: Part 2

(BQ) Part 2 book "Fundamentals of calculus" has contents: Integral calculus, techniques of integration, functions of several variables, series and summations, applications to probability. | 6 Integral Calculus Introduction Antiderivative as an Area Under a Curve Indefinite Integrals Example Integration Example More Integrations Initial Conditions Example Integrals with Initial Conditions Example Marginal Revenue and Marginal Cost with Initial Conditions Riemann Sums Example Determining Specified Points Example Area Under the Curve for f (x) = x2 Example Area Under a Graph Integral Calculus – The Fundamental Theorem Example Riemann Sums and Definite Integrals Example Evaluating Definite Integrals Example More on Evaluating Definite Integrals Example Definite Integrals and Areas Area Between Intersecting Curves Example Area Bounded by Curves Example More on Area Bounded by Curves More Applications Example Average Value Example EOQ − Economic Order Quantity Example Consumers’ Surplus Historical Notes — Georg Riemann 166 167 168 169 170 171 171 172 174 174 176 176 178 179 180 181 181 184 184 185 186 186 187 189 190 INTRODUCTION The calculus is composed of two main parts: the differential calculus, the subject of prior chapters, and the integral calculus, the subject of this chapter. The mathematical operation of integration arises in two contexts. One, as the opposite of differentiation – called antidifferentiation or antiderivatives. The other, as the area under a graph of a function – “an area under a curve!”. We briefly illustrate both as a preliminary to their study. Antidifferentiation is essentially synonymous with integration. If 3x2 is the derivative of 3 , for example, then x3 is the antiderivative of 3x2 . More precisely, x3 + C, C a constant, x is the antiderivative of 3x2 . This follows as the derivative of a constant is zero. Fundamentals of Calculus, First Edition. Carla C. Morris and Robert M. Stark. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc. Companion Website: .