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- integrate ƒ over the given region. ƒ(s, t) = e^s ln t over the region in the first quad-rant of the st-plane that lies above the curve s = ln t from t = 1 to t =2.Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates: dx /dt = 1 m/sec, dy/ dt = -2 m/sec, dz /dt = 1 m/sec. Find the rates at which the box’s (a) volume, (b) surface area, and (c) diagonal length s = 2x2 + y2 + z2 are changing at the instant when x = 4, y = 3, and z =2.1. Compute E yz dV , where E is the region above z 0, below z y, and inside x 2 y 2 4