26. Express the volume of the solid that is generated when the region bounded by the curves y = x^1/2, x = 0, y = 1, is revolved around the line y = 2 by: (a) a definite integral in which you will be integrating with respect to x; (b) a definite integral in which you will be integrating with respect to y. Then choose one of the two integrals and calculate the volume of the solid.

28. Express the volume of the solid that is generated when the region bounded by the curves y = x^1/2, y = x², is revolved around the line x = –3 by: (a) a definite integral in which you will be integrating with respect to x; (b) a definite integral in which you will be integrating with respect to y. Then choose one of the two integrals and calculate the volume of the solid.

30. Express the volume of the solid that is generated when the region bounded by the curves y = x², y = 0, x = 1, is revolved around the line y = –1 by: (a) a definite integral in which you will be integrating with respect to x; (b) a definite integral in which you will be integrating with respect to y. Then choose one of the two integrals and calculate the volume of the solid.

34. A ball of radius r is cut into two pieces by a horizontal plane a units above the center of the ball. Determine the volume of the upper piece by using the shell method.

38. (a) Sketch the region in the right half-plane that is outside the parabola y = x² and is between the lines y = x + 2 and y = 2x – 2. (b) The region in (a) is revolved around the y-axis. Use the method that you think is most practical to calculate the volume of the solid that is generated.