17-44. Solids of revolution Let R be the region bounded by the follow- ing curves. Find the volume of the solid generated when R is revolved about the given axis. 17. y = 2x, y = 0, and x = 3; about the x-axis (Verify that your answer agrees with the volume formula for a cone.) (3. 6) y = 2x R19. y = ex, y = 0, x = 0, and x = In 4; about the x-axis R In 4\f31. y = sin xon 0, a andy = 0; about the x-axis 1 - cos 2x ( Hint: Recall that sin x 2 32. y = sec x, x = 0. y = 0, and y = #; about the y-axis 33. y = sin xx = 0, y = "; about the y-axisPractice Exercises 9-30. Finding area Determine the area of the shaded region in the fol- lowing figures. 11. 18. 12. 19. 20 13. (Hinr: Find the intersection point by inspection.) 14. 22.Practice Exercises 9 34. Shell method Let & be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when & is revalued ahart indicated aris y Yex - ,y- 0; about the y-axis ily= (1+ x] ,y= 0,x = 0, and x - 2; about the y-axis 11. y = lr, y = 3, and x = 0; about the y-axis (Use integration and check your answer using the volume formula for a cone.) 12 yo-r + Ax+2,y=x - fix + 10; about the y-axis15. 104 - x,Y 2, and * 0 about the x-axis R1 21-30. Arc length by calculator a. Write and shoplify the integral that gives the are length of the fol- lowing curves on the given interval b. If necessary, lise technology to evaluate or approximate the internal 21. per. for-Isis| 2. y= sins, for0 sIST 13. y= Inc. for | $.$ 4 for-I sxsi 15. *= Vy - 2, for 3 5 754 16. = for1 5x54 17. y = cos r, for O S 1 5 7 I 1 for -5 y 5 5