Module 4 – Integration Topic 1: Anti-differentiation Integration – The main idea Basic Integration (part 1) Basic Integration (part 2) Applications of Antidifferentiation Finding Total Cost from Marginal Cost Raindrop Problem – acceleration, velocity, position Topic 2: Antiderivatives as Areas Summations and Areas – The Main Idea Riemann Sums and Areas Riemann Sums and Areas – Ex.2 Using Geometry to Evaluate Definite Integrals Topic 3: Area, Definite Integrals, and FTC Fundamental Theorem of Calculus (FTC) – The Main Idea More Examples of Areas and FTC Total Value Application Problems (MTH 263) Evaluating a Definite Integral using Summations Fundamental Theorem of Calculus (FTC) (Part 2) example Differential Equation and Exponential Growth example Topic 4: Properties of Definite Integrals Properties of Definite Integrals Area Between Two Curves Area Between Two Curves – Another Example Shaded Area Example Average Value of a Function Topic 5: Integration by Substitution Integration by Substitution – The Main Idea Integration by Substitution – A short, easy example Integration by Substitution – More Examples Integration by Substitution – Even More Examples Integration by Substitution – Two Short Examples Integration by Substitution – Application Problem
