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Suppose the function y = h(x) is nonnegative and continuous on [o,], which implies that the area bounded by the graph of h and the
Suppose the function y = h(x) is nonnegative and continuous on [o,], which implies that the area bounded by the graph of h and the x-axis on [o, p] equals h(x) dx or | y dx. If the graph of y = h(x) on [a,] is traced exactly once by the parametric equations x = f(t), y = g(t), for a Sts b, then it follows by substitution that the area bounded by h is given by the equation below. Jan(x) ax= Jay ax= = ], (t) f'(t) at, if a = f(a) and B =f(b) or Jon(x) ax = ] , 9(1 ) f' (1 ) at , if a = f (b ) and B = f(a ) Find the area under one arch of the cycloid x = 15(t - sin t), y = 15(1 - cost)
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