String Worldsheet Area

Consider a relativistic string lying on the y-axis at time τ=0\tau = 0, stretching from y=0y=0 to y=1y=1. The string is parameterized so that one endpoint is at σ=0\sigma=0 and the other is at σ=1\sigma=1, and so that τ=t\tau = t. Now allow the string to propagate from time τ=0\tau = 0 to time τ=1\tau = 1, leaving the string fixed on the y-axis. Find the area of the resulting string worldsheet.

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