1. Calculus II (MAT 146) Dr. Day Monday August 21, 2017
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
Monday, August 21, 2017
MAT 146

2. Front of Room Table 1 Table 4 Table 3 Table 2 Table 5 Seating by Group
Monday, August 21, 2017
MAT 146
Seating by Group

3. Calculate: Derivatives and Integrals
Monday, August 21, 2017
MAT 146

4. Making Connections CHANGE ACCUMULATE CALCULUS! PRE-CALCULUS! LIMITS
FUNCTIONS
ACCUMULATE
PRE-CALCULUS!
Monday, August 21, 2017
MAT 146

5. Big Ideas From Calc I
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MAT 146

6. Integration Techniques: Substitution
Monday, August 21, 2017
MAT 146

7. 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.
Monday, August 21, 2017
MAT 146

8. Integration Applications: Area Between Curves (6.1)
Monday, August 21, 2017
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9. Monday, August 21, 2017
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10. Area Between Curves
Calculate the area between the graphs of y = x2 + 1 and y = 1 – x for 0 ≤ x ≤ 1.
Monday, August 21, 2017
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11. Monday, August 21, 2017
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12. 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.
Monday, August 21, 2017
MAT 146

13. Wrapping It Up Admin Details Course Resources Assignments Info Sheet
Syllabus
Expectations
Course Resources
Textbook
WebAssign
CAS Calculators
Course Website:
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
Monday, August 21, 2017
MAT 146

14. Monday, August 21, 2017
MAT 146