3apart.Problem分析.PDFVIP

328 8 Applications of the Integral 21 Explain why the surface area is infinite when y = llx is cover the disk. Hint: Change to a unit sphere sliced by planes rotated around the x axis (1 6 x a).But the volume of 3apart. Problem 14 gives surface area n for each slice. Gabriels horn is It cant enough paint to 23 A watermelon (maybe a football) is the result of rotating paint its surface. half of the ellipse x = ficos t, y = sin t (which means x2+ 2y2= 2).Find the surface area, parametrically or not. 22 A disk of radius 1 can be covered by four strips of tape (width y). If the strips are not parallel, prove that they cant 24 Estimate the surface area of an egg. 8.4 Probability and Calculus Discrete probability usually involves careful counting. Not many samples are taken and not many experiments are made. There is a list of possible outcomes, and a known probability for each outcome. But probabilities go far beyond red cards and black cards. The real questions are much more practical: 1. How often will too many passengers arrive for a flight? 2. How many random errors do you make on a quiz? 3. What is the chance of exactly one winner in a big lottery? Those are important questions and we will set up models to answer them. There is another point. Discrete models do not involve calculus. The number of errors or bumped passengers o