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

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Answer 1 · 2016-08-06T22:16:45

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

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

enter image source here

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

P: $x_P=-1 and y_P=3.37$ (I substituted $x=-1$ into the function);

O: $x_O=0 and y_O=0$ (the origin) as:

$d=sqrt((x_O-x_P)^2+(y_O-y_P)^2)$

$d=sqrt([0-(-1)]^2+[0-3.37]^2)=3.51$

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