Question

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

Answer 1

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

Explanation:

Arc Length

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

Use WolframAlpha to compute f'(x)

`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`