Calculus II (MAT 146) Dr. Day Monday, September 11, 2017

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Presentation transcript:

Calculus II (MAT 146) Dr. Day Monday, September 11, 2017 Return Quiz #5 Integration Method #2: Integration by Parts (Sec 7.1) Integration Method #3: Trig Integrals (Sec 7.2) Test #1: Friday! Monday, September 11, 2017 MAT 146

Undoing the Product Rule Monday, September 11, 2017 MAT 146

Integration by Parts Key Component of Integrand’s Two Factors For at least one factor, its derivative is “simpler” than the factor. For at least one factor, its anti-derivative is no more complex than the factor. Monday, September 11, 2017 MAT 146

Monday, September 11, 2017 MAT 146

You Choosing U: A Decision Algorithm L: log functions I: inverse trig functions A: algebraic functions T: trig functions E: exponential functions MAT 146 Monday, September 11, 2017

Review: Derivatives of Inverse Trig Functions Monday, September 11, 2017 MAT 146

Derivatives of Inverse Trig Functions: Co-Function Connections Monday, September 11, 2017 MAT 146

Trig Integrals Monday, September 11, 2017 MAT 146

More Trig Integrals! Monday, September 11, 2017 MAT 146

Which Roots Can You Simplify Mentally? Monday, September 11, 2017 MAT 146

Pythagorean Trig Identities Monday, September 11, 2017 MAT 146

Integrals Begging for Trig Substitutions! Monday, September 11, 2017 MAT 146

Using Trig Substitutions Monday, September 11, 2017 MAT 146

Trig Substitutions Monday, September 11, 2017 MAT 146

Integration Strategies: Which of These Can You Evaluate, WITHOUT Your CAS? Monday, September 11, 2017 MAT 146

Partial-Fraction Decomposition ?????? Monday, September 11, 2017 MAT 146

Partial-Fraction Decomposition Monday, September 11, 2017 MAT 146

What About… Improper Algebraic Fractions? Unfactorable Quadratics? Repeated Linear Factors? Monday, September 11, 2017 MAT 146