What is the arc length of $f(x) = x^2e^(3-x^2)$ on $x in [ 2,3]$ ?

Question

1394 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-03T11:11:25

$approx 1.8995$

We have
$f(x)=x^2*e^(3-x^2)$
so
$f'(x)=2xe^(3-x^2)+x^2e^(3-x^2)(-2x)$
so
$f'(x)=e^(3-x^2)*(2x-2x^3)$
We have to integrate

$int_2^3sqrt(1+(e^(3-x^2)*(2x-2x^3))^2)dx$
With a numerical method we get
$approx 1.8995$

What is the arc length of f(x) = x^2e^(3-x^2) f(x) = x^2e^(3-x^2) on x in [ 2,3] x in [ 2,3] ?