Calculus II (MAT 146) Dr. Day Wednesday Jan 17, 2018 Warmin’ Up: Derivatives and Integrals Who Are You? Calculus I: The Foundation of Calculus Derivatives: Rates of Change Integrals: Accumulation One of Many Methods of Integration: Substitution (5.5) Admin Details Course Resources Textbook WebAssign Course Website Assignments Wednesday, January 17, 2018 MAT 146

Calculate: Derivatives and Integrals Wednesday, January 17, 2018 MAT 146

Making Connections CHANGE ACCUMULATE CALCULUS! PRE-CALCULUS! LIMITS FUNCTIONS ACCUMULATE PRE-CALCULUS! Wednesday, January 17, 2018 MAT 146

Big Ideas From Calc I Wednesday, January 17, 2018 MAT 146

Integration Techniques: Substitution Wednesday, January 17, 2018 MAT 146

Evaluate each integral using u-substitution Evaluate each integral using u-substitution. Clearly indicate your connection between u and x. Include notation for the differentials du and dx throughout. Wednesday, January 17, 2018 MAT 146

Integration Applications: Area Between Curves (6.1) Wednesday, January 17, 2018 MAT 146

Wednesday, January 17, 2018 MAT 146

Area Between Curves Calculate the area between the graphs of y = x2 + 1 and y = 1 – x for 0 ≤ x ≤ 1. Wednesday, January 17, 2018 MAT 146

Wednesday, January 17, 2018 MAT 146

Area Between Curves: Strategies Graph the functions in question and identify the number of bounded regions as well as which function is greater than the other for each region. Determine the x-axis intervals (or y-axis intervals) for the bounded regions. The interval endpoints may be explicitly stated or can be determined using algebraic techniques, most typically by setting the two functions equal to each other. Draw in a typical rectangle and determine its area. This provides essential information for the area integral you need to create. For each bounded region, create a definite integral to represent the sum of the areas of an infinite number of typical rectangles. Evaluate this integral to determine the area of each bounded region. Note that your TI-89 or other CAS can be a useful tool for several components of your solution process. Wednesday, January 17, 2018 MAT 146

Wrapping It Up Admin Details Course Resources Assignments Info Sheet Syllabus Expectations Course Resources Textbook WebAssign CAS Calculators Course Website: http://math.illinoisstate.edu/day/courses/current/146/www.html Assignments WebAssign: Section 5.5 WebAssign: Two Review Assignments through Chapter 5 Review Quizzes Fri: Ch 3 Mon: Ch 3,4 Wed: Ch 3,4,5 Wednesday, January 17, 2018 MAT 146

Wednesday, January 17, 2018 MAT 146