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#