# What is the arclength of f(x)=-3x-xe^x on x in [-1,0]?

##### 1 Answer
Aug 6, 2016

I found $3.51$ but I used an approximation to a straight line.

#### Explanation:

I tried different ways but it didn't work.
The best came from observing the graph of your function betweem $x = - 1 \mathmr{and} x = 0$:

I noticed that it is almost a stright line; so I simply evaluated the length of a straight line between the two points:

P: ${x}_{P} = - 1 \mathmr{and} {y}_{P} = 3.37$ (I substituted $x = - 1$ into the function);

O: ${x}_{O} = 0 \mathmr{and} {y}_{O} = 0$ (the origin) as:

$d = \sqrt{{\left({x}_{O} - {x}_{P}\right)}^{2} + {\left({y}_{O} - {y}_{P}\right)}^{2}}$

$d = \sqrt{{\left[0 - \left(- 1\right)\right]}^{2} + {\left[0 - 3.37\right]}^{2}} = 3.51$