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Calculus II (MAT 146) Dr. Day Wednesday August 21, 2013

Calculus II (MAT 146) Dr. Day Wednesday August 21, 2013. Quiz #1: Calc I Ch 3 Review Integration: Do You Remember? (Chapter 5) Substitution : One of Many Methods of Integration (5.5) Integral A pplication: Area Between Curves (6.1) Admin Details Syllabus Sign-Off Expectations

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Calculus II (MAT 146) Dr. Day Wednesday August 21, 2013

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  1. Calculus II (MAT 146)Dr. Day Wednesday August 21, 2013 • Quiz #1: Calc I Ch 3 Review • Integration: Do You Remember? (Chapter 5) • Substitution: One of Many Methods of Integration (5.5) • Integral Application: Area Between Curves (6.1) • Admin Details • Syllabus Sign-Off • Expectations • Reminder: Course Resources • Textbook • WebAssign • PIP Packet • Instructor Website • Assignments MAT 146

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

  3. Integration Techniques: Substitution MAT 146

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

  5. MAT 146

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

  7. MAT 146

  8. 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

  9. Wrapping It Up • Course Resources • Textbook • WebAssign • PIP Packet #8 • CAS Calculators • Instructor Website: math.illinoisstate.edu/day/courses/current/146/www.html • Assignments • WebAssign Section 5.5 due Thurs 8/22 midnight • WebAssign Section 6.1 due Fri 8/23 midnight • WebAssign : Two Review Assignments through Chapter 5 (due Sept 1 and Sept 3) • Review Quizzes: Wed (Ch 3), Thurs (Ch 3,4), Fri (Ch 3,4,5) MAT 146

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