Find the length of the curve. x = 6t - 2t^3, y = 6t^2, 0 <= t <= 2
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First, we need to find the derivatives of x and y with respect to t: dx/dt = d(6t - 2t^3)/dt = 6 - 6t^2 dy/dt = d(6t^2)/dt = 12t Now, we need to find the length of the curve using the formula: L = ∫(√((dx/dt)^2 + (dy/dt)^2)) dt from 0 to 2 L = ∫(√((6 - 6t^2)^2 Show more…
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