Yet Another Calculus Text, 2007a

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CONTENTS
1.12.1 Acceleration.......................... 59
1.12.2 Concavity........................... 59
1.12.3 Thesecond-derivativetest.................. 60
2 Integrals 63
2.1 Integrals................................ 63
2.1.1 Thecaseofconstantacceleration.............. 67
2.2 Definiteintegrals ........................... 69
2.3 Propertiesofdefiniteintegrals.................... 72
2.4 Thefundamentaltheoremofintegrals ............... 75
2.5 Applicationsofdefiniteintegrals .................. 79
2.5.1 Areabetweencurves..................... 79
2.5.2 Volumes............................ 84
2.5.3 Arclength........................... 88
2.6 Sometechniquesforevaluatingintegrals .............. 91
2.6.1 Changeofvariable ...................... 91
2.6.2 Integrationbyparts ..................... 95
2.6.3 Some integrals involving trigonometric functions . . . . . 97
2.6.4 Changeofvariablerevisited.................104
2.7 The exponential and logarithm functions . .............110
2.7.1 Theexponentialfunction ..................110
2.7.2 The logarithm function . ..................114
2.7.3 Someapplications ......................119
Answers to Exercises 129
Index 140