9 FURTHER APPLICATIONS OF INTEGRATION

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CHAPTER 9 FURTHER APPLICATIONS OF INTEGRATION GROUP WORK 2 (Hydrostatic Pressure): Under Pressure HOMEWORK PROBLEMS Core Exercises: 1, 4, 13, 18, 19, 21, 26, 31, 35, 41 Sample Assignment: 1, 4, 10, 13, 14, 17, 18, 19, 21, 24, 26, 27, 31, 32, 35, 36, 38, 41, 44 Exercise D A N G 1 × × 4 × × 10 × × 13 × 14 × 17 × 18 × 19 × × 21 × × 24 × 26 × × 27 × × 31 × 32 × 35 × × 36 × 38 × × 41 × × 44 × 504
GROUP WORK 1, SECTION 9.3 TheFloatingCenter 1. Consider the region bounded by y = sec x, x =− 1 2 , x = 1 2 ,andthex-axis. y 2 y=sec x _1 0 1 x Computethecenterofmass,anddrawitonthefigure.(Hint: x = 0 by symmetry. y can be computed by evaluating a relatively simple integral.) 2. Now consider the region defined by y = sec x, x =− π 2 + ε, x = π 2 − ε, and the x-axis. y 4 y=sec x 2 ¹ _2 _ · 0 · ¹ _2 x Draw in the centers of mass for ε = 0.25 and for ε = 0.01. 3. Some define the center of mass to be the point where a region will balance. What does your second result mean physically in light of the above definition? 4. Make a conjecture about lim ε→0 y. What does this mean, physically? 505
Page 1 and 2: 9 FURTHER APPLICATIONS OF INTEGRATI
Page 3 and 4: SECTION 9.1 ARC LENGTH 6. y y 2.1 2
Page 5 and 6: SECTION 9.1 ARC LENGTH SPECIAL PROJ
Page 7 and 8: The Bizarre Coastline 3. As you pro
Page 9 and 10: GROUP WORK 2, SECTION 9.1 Cable Guy
Page 11 and 12: SPECIAL PROJECT FOR SECTION 9.1 How
Page 13 and 14: DISCOVERY PROJECT Arc Length Contes
Page 15 and 16: SECTION 9.2 AREA OF A SURFACE OF RE
Page 17 and 18: GROUP WORK 1, SECTION 9.2 Gabriel
Page 19 and 20: DISCOVERY PROJECT Rotating on a Sla
Page 21: SECTION 9.3 APPLICATIONS TO PHYSICS
Page 25 and 26: DISCOVERY PROJECT Complementary Cof
Page 27 and 28: SECTION 9.4 APPLICATIONS TO ECONOMI
Page 29 and 30: 9.5 PROBABILITY TRANSPARENCY AVAILA
Page 31 and 32: SECTION 9.5 PROBABILITY GROUP WORK
Page 33 and 34: Foretelling the Future 3. Now fill
Page 35 and 36: The Wheel of Fate 2. One young pers
Page 37 and 38: CHAPTER 9 SAMPLE EXAM 6. Let f (x)
Page 39 and 40: CHAPTER 9 SAMPLE EXAM SOLUTIONS 3.

9 FURTHER APPLICATIONS OF INTEGRATION

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