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5. The region R is bounded by the curves x = y? + 2, y = x - 4, and y = 0 (see figure). R a. Write a single integral that gives the area of R. Evaluate the integral. 2.5pts b. Write a single integral that gives the volume of the solid generated when R is revolved about the x-axis. Evaluate the integral. 2.5pts Ac. Write a single integral that gives the volume of the solid generated when R is revolved about the y-axis. Evaluate the integral. 2.5pts d. Suppose that S is a solid whose base is R and whose cross sections perpendicular to R and parallel to the x-axis are semicircles. Write a single integral that gives the volume of S. Evaluate it. 2.5pts 6. A spherical tank is filled with water (see figure). Find the work required to pump the water out of the spout. The density of water is 1000 kg/m' 5pts I m 3m