Solve the following problems, showing any necessary work. You only need to set up integrals to calculate the problems.

1. Let R be the region bounded by the curvesy=(x3)2 and y=49.
   1. [2 points] Set up integrals with respect to x and with respect to y which calculate the area of R. [which should be approximately 457.3]
   2. [2 points] The region R is rotated around the x-axis to form the solid S₁. Set up integrals using the Washer Method and the Cylindrical Shell Method to find the volume of S₁. Identify which method provides which integral. [84481.2]
   3. [1 point] The boundary of R consists of a line segment and part of a parabola. Find the length of the parabolic part. [99.9]
   4. [1 point] The region R is the base of a solid S₂. When cross-sections of S₂ are taken perpendicular to the y-axis, they are found to be triangles who base is horizontal, and whose height is three times their base. Find the volume of the solid S₂. [26891.2]
2. [1 point] A cable that weighs 5 kg/m is used to lift 800 kg of coal up a mine shaft 500 m deep. Find the work done, assuming that the weight of the container is negligible. [10.05 megajoules]