1. Consider the region R bounded by the curves y = 1, y = x, and x = 4. (a) (3 points) Sketch a graph of the region. (You should attempt this problem on your own first, but you may use Desmos to verify your answer.) (b) (4 points) Compute the area of the region R. (c) (3 points) Write, but do not evaluate, an integral which gives the volume of the solid whose base is R and whose cross-sections perpendicular to the x-axis are semi-circles. (d) (4 points) Compute the volume of the solid whose base is R and whose cross-sections perpendicular to the x-axis are squares. (e) (3 points) Write, but do not evaluate, an integral which gives the volume of the solid whose base is R and whose cross-sections perpendicular to the x-axis are equilateral triangles. (f) (4 points) Compute the volume of the solid whose base is R and whose cross-sections perpendicular to the y-axis are semicircles. (g) (4 points) Compute the volume of the solid formed by rotating R around the x-axis. (h) (3 points) Write, but do not evaluate, an integral which gives the volume of the solid formed by rotating R around the y-axis.