- Calculus, Volume 1: One Variable Calculus, with an Introduction to Linear Algebra
- Tom M. Apostol
- Second Edition
- 1967
- 978-1-119-49673-1
14.13 Exercises
- Show that the length of the curve $y = \cosh x$ joining the points $(0, 1)$ and $(x, \cosh x)$ is $\sinh x$ if $x > 0.$
- We saw in exercise 14 that the length of the curve $y = \cosh \frac{x}{c}$ from $x = 0$ to $x = a$ for some $a>0$ is: $$ s = c\sinh\frac{a}{c} $$ Setting $c = 1,$ we see that the arc length of the curve $y = \cosh t$ from $t = 0$ to $t = x,$ is $s = \sinh x. \quad \blacksquare$