Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 710: 38

$sinh 3$

$x=2+3t$, $y=cosh3t$ on $0\leq t\leq 1$ $x'=3$, $y'=3 sinh (3t)$ on $0\leq t\leq 2$ Length of the curve is given as: $L=\int_{0}^{1}\sqrt {(3)^2+(3 sinh (3t))^2} dt$ $=\int_{0}^{1} 3 (cosh 3t )dt$ $=sinh 3-sinh 0$ $=sinh 3$