The ends of a "parabolic" water tank are the shape of the region inside the graph of  y = x2  for  0 ≤ y ≤ 9 ; the cross sections parallel to the top of the tank (and the ground) are rectangles. At its center the tank is 9 feet deep and 6 feet across. The tank is 6 feet long. Rain has filled the tank and water is removed by pumping it up to a spout that is 4 feet above the top of the tank. Set up a definite integral to find the work W that is done to lower the water to a depth of 7 feet and then find the work. [Hint: You will need to integrate with respect to y.]

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A: Solution:-