1. 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

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

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

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

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

6. 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

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

8. Wednesday, January 17, 2018
MAT 146

9. 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

10. Wednesday, January 17, 2018
MAT 146

11. 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

12. 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
Wednesday, January 17, 2018
MAT 146

13. Wednesday, January 17, 2018
MAT 146