Page 11 - Calculus Demystified
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x 7.3 Substitution Contents
207
7.4 Integrals of Trigonometric Expressions 210
CHAPTER 8 Applications of the Integral 217
8.1 Volumes by Slicing 217
8.1.0 Introduction 217
8.1.1 The Basic Strategy 217
Examples
8.1.2
219
8.2 Volumes of Solids of Revolution 224
8.2.0 Introduction 224
8.2.1 The Method of Washers 225
8.2.2 The Method of Cylindrical Shells 228
8.2.3 Different Axes 231
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8.3 Work 233
8.4 Averages 237
8.5 Arc Length and Surface Area 240
8.5.1 Arc Length 240
8.5.2 Surface Area 243
8.6 Hydrostatic Pressure 247
8.7 Numerical Methods of Integration 252
8.7.1 The Trapezoid Rule 253
8.7.2 Simpson’s Rule
256
Bibliography 263
Solutions to Exercises 265
Final Exam 313
Index 339
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