What is the arc length of $f(x)=(1-x)e^(4-x)$ on $x in [1,4]$ ?

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Answer 1 · 2016-10-24T18:28:15

$int_1^4 sqrt(1 + ((x - 2)e^(4 -x))^2)dx = ≈12.4385$

$s = int_a^b sqrt(1 + (f'(x))^2)dx$

$f'(x) = (x - 2)e^(4 -x)$

The indefinite integral cannot be done using standard mathematical functions but I was able to make WolframAlpha evaluate the definite integral

$int_1^4 sqrt(1 + ((x - 2)e^(4 -x))^2)dx = ≈12.4385$

What is the arc length of f(x)=(1-x)e^(4-x) f(x)=(1-x)e^(4-x) on x in [1,4] x in [1,4] ?