Arc Length of an Exponential Function

Question

I have this function;

$f(x)=1.982545 - 1.982545e^{5.944638x}$

I need to find the arc length from 0 to 1.98 ($x$ values obviously).

I know some of the math behind it but not nearly enough to do it on my own. It would be great if in answering the question it could be explained at a basic level and with all/most of the formulae needed to arrive at the final answer. Thanks!

Answer 1

HINT

Recall that for a function $f(x)$ the arch length between $x=x_1$ and $x=x_2$ is given by

$$L=\int_{x_1}^{x_2} \sqrt{1+[f'(x)]^2}\, dx$$

and that

$$f(x)=a+ae^{bx}\implies f'(x)=abe^{bx}$$