Find the exact length of the curve

x = e^{t} + e^{−t}, y = 5 − 2t, 0 ≤ t ≤ 2

x = e^t + e^-t

dx = (e^t - e^-t)dt

dx² = e^(2t) -2 + e^(-2t) y = 5 -2t,

dy = -2dt

dy² = 4 dx² + dy² = e^(2t) -2 + e^(-2t) + 4

= e^(2t) +2 + e^(-2t)

= (e^t + e^-t)² the length is given by: s = ∫(dx² + dy²)^(1/2)dt

= ∫[(e^t + e^-t)²]^(1/2)dt

=∫(e^t + e^-t)dt s = (e^t - e^-t) (0 to 2)

= (e^2 - e^0)-(e^-2 - e^0)

= 7.2537

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