What is the arc length of $f (x) = x - x e^{x}$ $f(x) = x-xe^(x)$ on $x \in [2, 4]$ $x in [ 2,4]$ ?

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Answer 1 · 2017-04-01T12:30:32

$L = \int_{2}^{4} \sqrt{1 + {(1 - e^{x} - x e^{x})}^{2}} d x \approx 201.361$ $L=int_2^4sqrt(1+(1-e^x-xe^x)^2)dxapprox201.361$

The arc length of $f$ $f$ on $x \in [a, b]$ $x in [a,b]$ 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.

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