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Calculus II (MAT 146) Dr. Day Wednesday August 20, 2014

Calculus II (MAT 146) Dr. Day Wednesday August 20, 2014. Quiz #1: Calc I Ch 3 Review Mathematizing Situations Integrals (Chapter 5) Admin Details Syllabus Sign-Off Expectations XC Opportunity Reminder: Course Resources Textbook WebAssign PIP Packet #19 Course Website Assignments.

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Calculus II (MAT 146) Dr. Day Wednesday August 20, 2014

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  1. Calculus II (MAT 146)Dr. Day Wednesday August 20, 2014 • Quiz #1: Calc I Ch 3 Review • Mathematizing Situations • Integrals (Chapter 5) • Admin Details • Syllabus Sign-Off • Expectations • XC Opportunity • Reminder: Course Resources • Textbook • WebAssign • PIP Packet #19 • Course Website • Assignments MAT 146

  2. Making Connections CALCULUS! CHANGE LIMITS FUNCTIONS ACCUMULATE PRE-CALCULUS! MAT 146

  3. Calculate: Derivatives and Integrals MAT 146

  4. Integration Techniques: Substitution MAT 146

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

  6. Integration Applications: Area Between Curves (6.1) MAT 146

  7. MAT 146

  8. Area Between Curves Calculate the area between the graphs of y = x2 + 1 and y = 1 – x for 0 ≤ x ≤ 1. MAT 146

  9. MAT 146

  10. 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. MAT 146

  11. Assignments • Course Resources • Textbook • WebAssign • PIP Packet #19 • CAS Calculators • Website: math.illinoisstate.edu/day/courses/current/146/www.html • Assignments • WebAssign Section 5.5 due Fri 8/22 midnight • WebAssign : Two Review Assignments through Chapter 5 • Review Quizzes: Today (Ch 3), Thurs (Ch 3,4), Fri (Ch 3,4,5) MAT 146

  12. MAT 146

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