Post surfing you relax on the beach, then get ready to hike the mountain located at the center of the island. After you reach the mountain top you come across an eerie cave which is shaped in the form of a semi-paraboloid. The equation governing the surface of the outer wall of the cave is given by z(x, y) = x 2 y 2 + k 2 , z > 0, k is a real positive constant.Consider a vector field G~ (x, y, z) = x x + y y + z z. Set up the integral of this vector field over the surface of the cave. Your final answer should be a double integral in terms of x and y. The double integral's limits must be in terms of x and other constants.