(8). Region R is bounded above by y = x + 1, below by the x-axis, and by the lines x = 1 and x = 4. Use this region to solve the following two problems: (a). Region R is revolved about the x-axis. Find its exact volume. (b). Region R is revolved about the y-axis. Find its exact volume. (9). Determine the arc-length of the curve y = x - x for 1 s x $ 4. You may leave your answer as an approximate to three-decimal place accuracy. 10. 13. An object has the following shape: its base is the parabola x = y for 0 S x $ 16. For each x, the cross sections are triangles that span the parabola from its positive coordinate to its negative coordinate, with height equal to the length of the span, that is, s = h. You can assume the apex of each triangle is directly over the x-axis. The resulting object has a "ridgeback" shape (see figure). Set up an integral and find this object's volume. triangular cross-section s=span =height parabolic base 11. 14. A cylindrical tank measures 4 feet long and has a circular end with radius of 1 ft. It is lying on its side. Water is filled to the top. Determine the work needed to pump the water out the top of the tank. Density of water: 62.4 05. At3. State your answer to three decimal place accuracy. 1 ft 4 ft