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Real-World Applicationshard
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A dam has a vertical cross-section in the shape of a parabola y=x2y = x^2y=x2 for 0lexle20 \\le x \\le 20lexle2 meters (width www is constant at 10 meters). The water depth is d=4d = 4d=4 meters. The hydrostatic force on the dam wall is given by F=int0drhog(d−y)wdsF = \\int_0^d \\rho g (d - y) w dsF=int0d​rhog(d−y)wds, where ds=sqrt1+(dx/dy)2dyds = \\sqrt{1 + (dx/dy)^2} dyds=sqrt1+(dx/dy)2dy. Which integral represents the total hydrostatic force?