Question

What is the arc length of `f(x) = x-xe^(x)` on `x in [ 2,4]`?

Answer 1

`L=int_2^4sqrt(1+(1-e^x-xe^x)^2)dxapprox201.361`

Explanation:

The arc length of `f` on `x in [a,b]` is given by

`L=int_a^bsqrt(1+(f'(x))^2)dx`

Here, `f(x)=x-xe^x` so `f'(x)=1-e^x-xe^x`. Then,

`L=int_2^4sqrt(1+(1-e^x-xe^x)^2)dxapprox201.361`

Which can be found with a calculator or Wolfram Alpha.