What is the arc length of f(x)= 1/sqrt(x-1) on x in [2,4] ?
1 Answer
Mar 4, 2016
Explanation:
f'(x) = -1/{2 sqrt{ (x-1)^{3} } }
The length is given by
L = int_2^4 sqrt{1 + f'(x)^2} "d"x
= int_2^4 sqrt{1 + (-1/{2 sqrt{ (x-1)^{3} } })^2} "d"x
= int_2^4 sqrt{1 + 1/{4 (x-1)^3 } } "d"x
~~ 2.05411
