Question

How do you find the arc length of the curve `f(x)=coshx` over the interval [0, 1]?

Answer 1

I used WolframAlpha
`s = int_0^1 sqrt(1 + sinh^2(x))dx ≈ 1.1752`

Explanation:

From the reference on Arc Length we write the equation:

`s = int_a^b sqrt(1 + (dy/dx)^2)dx`

Given: `a = 0, b = 1, and y = cosh(x)`

We know that `(dy)/(dx) = sinh(x)`

The arc length integral is:

`s = int_0^1 sqrt(1 + sinh^2(x))dx ≈ 1.1752`