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#
