1. The region bounded by the curve y = x2 + 2 and the straight line y = 2x + 5 is revolving about the Ox-axis to generate a solid. Find the volume of the solid.
2. The region bounded by the curve x = √y and the straight line x = 2y is revolving about the Oy-axis to generate a solid. Find the volume of the solid.
3. The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2. The cross sections perpendicular to the x-axis are circular disks whose diameters run from the parabola y = x2 to the parabola y = 4 - x2. Find the volume of the solid.
4. Find the length of the curve
y = (x3 /12) - (1 / x), 2 ≤ x ≤ 3.
Find the area of the surface generated by revolving the curve y = √x, 3 ≤ x ≤ 8, about the Ox-axis.