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The ends of a quot;parabolicquot; water tank are the shape of the region inside the graph of y = x2 for 0 y 9 ; the cross sections parallel to the...
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. It is 9 feet long. Rain has filled the tank and water is removed by pumping it up to a pipe 2 feet above the top of the tank. Set up an iterated integral to find the work W that is done to lower the water to a depth of 6 feet and then find the work. [Hint: You will need to integrate with respect to y.]
