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Find the exact length of the curve.

x=(y^4)/8+1/(4y^2), 1 ≤ y ≤ 2.

1 answer

y' = y^3/2 - 1/(2y^3)
1+y'^2 = (y^6+1)^2/4y^6
so, the arc length is

s = 1/2 ∫[1,2] y^3 + 1/y^3 dy = 33/16
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