What is the arclength of $(t-1,t/(t+5))$ on $t in [-1,1]$ ?

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Answer 1 · 2018-04-20T16:29:12

The arc length is approximately $2.05$ units.

The arc length of parametric functions is

$int_(-1)^1 sqrt((dy/(dt))^2 + ((dx)/(dt))^2) dt$

$int_(-1)^1 sqrt(1 + ((t + 5 - t)/(t + 5)^2)^2) dt$

$int_(-1)^1 sqrt(1 + 25/(t + 5)^4) dt$

Use a calculator to evaluate this tricky integral. Thus

$I = 2.05$

Hopefully this helps!

What is the arclength of (t-1,t/(t+5))(t-1,t/(t+5)) on t in [-1,1]t in [-1,1]?