A mountain in the ocean is bounded by the ocean floor z = 0 and the cone z = 4 - 2 √ x 2 + y 2. Suppose the heat flow in and around the mountain is described by the vector field F (x, y, z) = y 2 (x + sin y) i + z cos xj + x 2 zk. Calculate the flux of heat flowing out of the mountain. Hint: use the divergence theorem.
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