A small dam is constructed across a stream. vertical cross section of the stream is y=2x^2. the dam is 4 ft tall. Set up and evaluate an integral that estimates the hydrostatic force on the damn when the water is all the way to the top. Force=Pressure*Area and Water weighs 62.5lb/cubic foot.

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here is a picture of the vertical cross section

Let's cut the water into n layers of thickness of x*subk, x being the kth level. The work done is Fx

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