Find the arc length of the curve r(t) on the interval [−π/3].

geduiwelh

geduiwelh

Answered question

2021-03-09

Given r(t)=sec2t,sint, find the arc length of the curve r(t) on the interval [π3]

Answer & Explanation

liannemdh

liannemdh

Skilled2021-03-10Added 106 answers

Let y=f(x),axb be the given curve. The definite integral determines the arc length LL of such a curve.
=ab1+[(x)]2 dx 
Let x=g(t),y=h(t) where c≤x≤d be the parametric equations of the curve y=f(x).
After that, the curve's arc length is determined by
L=cd( dx  dt )2+( dy  dt )2 dt 
Here x(t)=sec2t,y(t)=sint where π/3xπ/3 be the parametric equations of the curve y=f(x).

Consequently, the curve's arc length is determined by

L=π/3π/3sec2t)2+sint)2dt=π/3π/3sec22t+sin2tdt

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