5_2_Natural_Log&Integration

5_2_Natural_Log&Integration - 5.2 The Natural...

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Unformatted text preview: 5.2 The Natural Logarithm: Integration Introduction HW: 5.2 #113, 17, 2133, 37, 39, 4345,47,5359,67,69 1. y = ln x 1. dy/dx = 2. y = ln 2x 2. dy/dx = 3. y = ln (x2 +2) 3. dy/dx = Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 1 5.2 The Natural Logarithm: Integration Introduction 1. y = ln x 1. dy/dx = 2. y = ln 2x 2. dy/dx = 3. y = ln (x2 +2) 3. dy/dx = Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 G. Battaly, 2011 2 5.2 The Natural Logarithm: Integration Introduction 3. y = ______ ? 3. dy/dx = 2x+ 3 x2+ 3x Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework Part 1 Homework Part 2 Title: Intro (2 of 12) 5.2 The Natural Logarithm: Integration Introduction 3. y = ______ ? 3. dy/dx = 2x+ 3 x2+ 3x Let u = _________________ Then du/dx = _________________ and remembering we need to consider the integral: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: Intro (3 of 12) 5.2 The Natural Logarithm: Integration Log Rule for Integration Let u be a differentiable function of x. Then: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: Integration and ln (4 of 12) 5.2 The Natural Logarithm: Integration What about ? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: What about? (5 of 12) 5.2 The Natural Logarithm: Integration Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (6 of 12) 5.2 The Natural Logarithm: Integration even problems Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (7 of 12) 5.2 The Natural Logarithm: Integration even problems Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (8 of 12) 5.2 The Natural Logarithm: Integration even problems Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (9 of 12) 5.2 The Natural Logarithm: Integration even problems required to factor numerator but only helps if one factor is (x2). otherwise cannot reduce to lowest terms But, can do long division Or Synthetic Division: PowerPoint (click Read Only) Step by Step Instructions Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (10 of 12) 5.2 The Natural Logarithm: Integration even problems Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (11 of 12) 5.2 The Natural Logarithm: Integration even problems Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (12 of 12) ...
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