CalcII_Complete_Assignments

CalcII_Complete_Assignments - CALCULUS II Assignment...

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CALCULUS II Assignment Problems Paul Dawkins
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Calculus II Table of Contents Preface ........................................................................................................................................... iii Outline ........................................................................................................................................... iii Integration Techniques ................................................................................................................. 5 Introduction ................................................................................................................................................ 5 Integration by Parts .................................................................................................................................... 5 Integrals Involving Trig Functions ............................................................................................................. 6 Trig Substitutions ....................................................................................................................................... 8 Partial Fractions ........................................................................................................................................ 11 Integrals Involving Roots .......................................................................................................................... 12 Integrals Involving Quadratics .................................................................................................................. 13 Integration Strategy ................................................................................................................................... 13 Improper Integrals ..................................................................................................................................... 14 Comparison Test for Improper Integrals ................................................................................................... 15 Approximating Definite Integrals ............................................................................................................. 16 Applications of Integrals ............................................................................................................. 17 Introduction ............................................................................................................................................... 17 Arc Length ................................................................................................................................................ 17 Surface Area .............................................................................................................................................. 18 Center of Mass .......................................................................................................................................... 20 Hydrostatic Pressure and Force ................................................................................................................. 20 Probability ................................................................................................................................................. 23 Parametric Equations and Polar Coordinates .......................................................................... 25 Introduction ............................................................................................................................................... 25 Parametric Equations and Curves ............................................................................................................. 25 Tangents with Parametric Equations ......................................................................................................... 27 Area with Parametric Equations ................................................................................................................ 28 Arc Length with Parametric Equations ..................................................................................................... 28 Surface Area with Parametric Equations ................................................................................................... 29 Polar Coordinates ...................................................................................................................................... 30 Tangents with Polar Coordinates .............................................................................................................. 32 Area with Polar Coordinates ..................................................................................................................... 32 Arc Length with Polar Coordinates ........................................................................................................... 32 Surface Area with Polar Coordinates ........................................................................................................ 33 Arc Length and Surface Area Revisited .................................................................................................... 33 Sequences and Series ................................................................................................................... 34 Introduction ............................................................................................................................................... 34 Sequences .................................................................................................................................................. 34 More on Sequences ................................................................................................................................... 35 Series – The Basics ................................................................................................................................... 36 Series – Convergence/Divergence ............................................................................................................ 37 Series – Special Series .............................................................................................................................. 38 Integral Test .............................................................................................................................................. 39 Comparison Test / Limit Comparison Test ............................................................................................... 40 Alternating Series Test .............................................................................................................................. 41 Absolute Convergence .............................................................................................................................. 42 Ratio Test .................................................................................................................................................. 42 Root Test ................................................................................................................................................... 43 Strategy for Series ..................................................................................................................................... 44 Estimating the Value of a Series ............................................................................................................... 44 Power Series .............................................................................................................................................. 45 Power Series and Functions ...................................................................................................................... 45 Taylor Series ............................................................................................................................................. 46 Applications of Series ............................................................................................................................... 47 © 2007 Paul Dawkins i
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