Please solve 31 and 32 only 31. In the Appendix to Chapter 12 we described the cycloid, which has theparametric representation* = u(t) = a(t – sin t), y = v(t) = a(1 – cos t).(a) Find the length of one arch of the cycloid. [Answer: 8a).(b) Recall that the cycloid is the graph of v o u. Find the area underone arch of the cycloid by using the appropriate substitution in fand evaluating the resultant integral. (Answer: 3ma|Problems 32 through 44 use the material from Appendix 2 to Chapter 13.32. (a) Find the volume of the solid obtained by revolving the regionbounded by the graphs of f(x) = x and f(x) = x' around the hori-zontal axis.(b) Find the volume of the solid obtained by revolving this same regionaround the vertical axis.33. Find the volume of a sphere of radius r.34. When the ellipse consisting of all points (x, y) with x/a + y*/6? = 1 isrotated around the horizontal axis we obtain an "ellipsoid of revolu-tion" (Figure 2). Find the volume of the enclosed solid.FIGURE 2

Answered: Image /qna-images/answer/c3abcf25-165c-4ae1-a596-3dbd01cdf081.jpg

31. In the Appendix to Chapter 12 we described the cycloid, which has the parametric representation x = u(t) = alt – sin t), y = v(t) = a(1 – cos t). (a) Find the length of one arch of the cycloid. [Answer: 8a). (b) Recall that the cycloid is the graph of v o u. Find the area under one arch of the cycloid by using the appropriate substitution in Sf and evaluating the resultant integral. (Answer: 3ma'| Peoblems 32 throuh 44 vse the material from Annendiy 2 to Chanter 13

31. In the Appendix to Chapter 12 we described the cycloid, which has the parametric representation x = u(t) = alt – sin t), y = v(t) = a(1 – cos t). (a) Find the length of one arch of the cycloid. [Answer: 8a). (b) Recall that the cycloid is the graph of v o u. Find the area under one arch of the cycloid by using the appropriate substitution in Sf and evaluating the resultant integral. (Answer: 3ma'| Peoblems 32 throuh 44 vse the material from Annendiy 2 to Chanter 13

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.3: Implicit Differentiation

Problem 42E

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