What is the arc length of f(t)=(ln(1/t) ,5-lnt) over t in [3,4] ?
1 Answer
Jun 28, 2018
Explanation:
f(t)=(ln(1/t),5-lnt)=(-lnt,5-lnt)
f'(t)=(-1/t,-1/t)
Arc length is given by:
L=int_3^4sqrt(1/t^2+1/t^2)dt
Simplify:
L=sqrt2int_3^4 1/tdt
Integrate directly:
L=sqrt2[lnt]_3^4
Insert the limits of integration:
L=sqrt2ln(4/3)