(47) A rectangle is inscribed in the area under the graph of f(x) = e-ª² so that one of its sides is on the positive y-axis, one side is on the positive x-axis and its upper right-hand corner is on the curve f(x) = e-² (see the figure below). Find the exact value of the area of the largest rectangle. Show your work. y = exp(-x^2)

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