Question

What is the arclength of `(sqrtt,1/sqrt(t^2+3))` on `t in [1,2]`?

Answer 1

`approx 0.431873`

Explanation:

We have
`x(t)=sqrt(t)`
then
`x'(t)=1/(2*sqrt(t))`
`y(t)=1/sqrt(t^2+3)`

then
`y'(t)=-t/sqrt(t^2+3)^3`
So we get the integral
`int_1^2sqrt(1/(4*t)+t^2/(3+t^2)^3)dt`
I have found only a numerical value:

`approx 0.431873`