The ends of a "parabolic" water tank are the shape of the region inside the graph of y = x2 for 0 ≤ y ≤ 4 ; the cross sections parallel to the top of the tank (and the ground) are rectangles. At its center the tank is 4 feet deep and 4 feet across. The tank is 8 feet long. Rain has filled the tank and water is removed by pumping it up to a spout that is 3 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 3 feet and then find the work. [Hint: You will need to integrate with respect to y.]
Added by Tamara W.
Step 1
Let y measure vertical distance from the bottom of the tank, so that y = 0 is the bottom and y = 4 is the top. The ends of the tank are given by the parabola x² = y (or y = x²); for a given y the x‐coordinate runs from –√y to √y, so the width of the tank at height Show more…
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