The length of the curve equals ∫_{0}^{2} √( (x'_{t})^{2} + (y'_{t})^{2}) dt = ∫_{0}^{2} √( (e^{t } – e^{–t } )^{2} + (-2)^{2}) dt =

∫_{0}^{2 } √( e^{2t } – 2 + e^{–2t } + 4) dt = ∫_{0}^{2} (e^{t } + e^{–t }) dt = (e^{t } – e^{–t })]_{0}^{2} = e^{2 } – e^{–2 }

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