# calculus

Find the arc length of the given function/curve on the given interval.
y=ln(x-sqrt(x^(2)-1)); x ϵ [1, sqrt(2)]

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1. y = ln(x-√(x^2-1))
y' = 1/x-√(x^2-1) * (1-x/√(x^2-1))
= -1/√(x^2-1)

so, the arc length is

∫[1,√2] √(1+y'^2) dx
= ∫[1,√2] √(1+1/(x^2-1)) dx
= ∫[1,√2] x/√(x^2-1) dx
. . .

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