Need some help with problems 15 (uses figure 8.3) and 34(on the bottom of the page).

Exercises 12-17 refer to the regions marked in Figure 8.3. Set up, but do not evaluate, an integral that represents the volume obtained when the region is rotated about the given axis. y=x1/3 2 (8,2) R R, R. x = 4y Figure 8.3 12. R, about the x-axis 13. R, about the y-axis 14. R, about the line y = -2 15. R; about the line x = 10 16. R, about the line y = 3 17. R, about the line x = -3 18. Find the volume of the region in Figure 8.4, given that the radius, r of the circular slice at his r = Vh. 12 Ah h Figure 8.4 4 Chapter 8 REVIEW MATERIAL AND PROJECTS 19. Find, by slicing, the volume of a cone whose height is 3 cm and whose base radius is 1 cm. Slice the cone as shown in Figure 8.6 on page 404. For the curves described in Exercises 20-21, write the integral that gives the exact length of the curve; do not evaluate it. 20. One arch of the sine curve, from x = 0 to x = x. 21. The ellipse with equation (x /a] ) + (y?/b?) = 1. In Exercises 22-23, find the arc length of the function from x = 0 to x = 3. Use a graph to explain why your answer is reasonable. 22. f(x) = sin x 23. f(x) = 5x2 For Exercises 24-26, find the arc lengths. 24. f(x) = V1 - x2 from x = 0 to x = 1 25. f(x) = e' from x = 1 to x = 2 26. f(x) = =x' + - from x = 1 to x = 2. In Exercises 27-28, find the length of the parametric curves. Give exact answers if possible. 27. x = 3 cost, y = 2 sint, for 0 S t S 2x. 28. x = 1 + cos(21), y = 3 + sin(2t), for 0 St S n. In Exercises 29-33, let f(x) = x", for x 2 0 and p > 1. Note that f(0) = 0, f(1) = 1, and f is increasing with a concave-up graph. Use geometrical arguments to order the given quantities. 29. () dx and 30. S'() dx and 31. ( 5 '(0)dx and ; 32. * ((x) dx and 33. [ Vi+('() dx and VZ PROBLEMS 34. (a) Find the area of the region between y = x and y = 2x. (b) Find the volume of the solid of revolution if this region is rotated about the x-axis. (c) Find the length of the perimeter of this region