4. Let R be the region bounded by the linesx - 2y = 0, x - 2y = -4, x + y = 4, and x + y = 1as shown in Figure 2. Evaluate the double integral (15 分)

1. In the engine shown in Figure 1, a 7-inch connecting rod is fastened to a crank of radius 3 inches. The crankshaft rotates counterclockwise at a constant rate of 200 rpm (revolutions per minute). Find the velocity (i.e., dx/dt) of the piston when θ = π/3. (15 分) Figure 1. The velocity of a piston is related to the angle of the crankshaft.