Calculus II (MAT 146)Dr. Day Friday August 21, 2015

Quiz #1: Chapter 3 Review

Calculus I: The Foundation of Calculus Derivatives: Rates of Change Integrals: Accumulation

One of Many Methods of Integration: Substitution (5.5)

Syllabus Questions?

Review: Course Resources Textbook, WebAssign, Course Website, Tutoring

Assignments

Friday, August 21, 2015 MAT 146

MAT 146

Making Connections

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CHANGE

ACCUMULATE

LIMITS

FUNCTIONS

CALCULUS!

PRE-CALCULUS!

MAT 146

Big Ideas From Calc I

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MAT 146

Integration Techniques:

Substitution

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MAT 146Friday, August 21, 2015

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

Integration Applications: Area

Between Curves (6.1)

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MAT 146

Area Between Curves

Calculate the area between the graphs of y = x2 + 1 and y = 1 – x for 0 ≤ x ≤ 1.

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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.

Friday, August 21, 2015

MAT 146

Review: Admin Details and Course Resources

Assignments WebAssign: Sections 5.5 and 6.1 WebAssign: Two Review Assignments through Chapter 5 Review Quizzes

Today: Ch 3 Fri: Ch 3,4 Mon: Ch 3,4,5

Wrapping It Up

Friday, August 21, 2015

MAT 146Friday, August 21, 2015