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

Oct 24, 2016

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

#### Explanation:

$s = {\int}_{a}^{b} \sqrt{1 + {\left(f ' \left(x\right)\right)}^{2}} \mathrm{dx}$

$f ' \left(x\right) = \left(x - 2\right) {e}^{4 - x}$

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