Hans Georg Schaathun
Oktober 2016
$$\Delta s = \sqrt{ (\Delta x)^2 + (\Delta y)^2 }$$
$$\Delta s = \sqrt{ 1 + \bigg(\frac{\Delta y}{\Delta x}\bigg)^2 }\Delta x$$
$$\frac{\Delta y}{\Delta x} = f'(c)$$
$$ x_1 \le c \le x_2$$
$$\Delta s = \sqrt{ 1 + \big(f'(c)\big)^2 }\Delta x$$
$$\Delta s = \sqrt{ 1 + \bigg(\frac{\Delta y}{\Delta x}\bigg)^2 }\Delta x$$
$$s \approx \sum_{i=1}^n \Delta s_i = \sum_i \sqrt{ 1 + \big(f'(c_i)\big)^2 }\Delta x$$
$$s = \int_{x_{\textrm{start}}^{x_{\textrm{slutt}} ds = \int_{x_{\textrm{start}}^{x_{\textrm{slutt}} \sqrt{ 1 + \big(f'(x)\big)^2 } dx$$
$$ds = \sqrt{ 1 + \big(f'(x)\big)^2 } dx$$