Verified answer

dy/dx = (1/8)(-2x + 8/x) = (1/4)(-x + 4/x).

So, √(1 + (dy/dx)^2)

= √(1 + (1/16)(x^2 - 8 + 16/x^2))

= √(1/16)(x^2 + 8 + 16/x^2))

= √(1/16)(x + 4/x)^2)

= (1/4)(x + 4/x), since x > 0.

Hence, the arc length equals

∫(x = 3 to 8) (1/4)(x + 4/x) dx

= (1/4)(x^2/2 + 4 ln x) {for x = 3 to 8}

= (1/8)(x^2 + 8 ln x) {for x = 3 to 8}

= (1/8) [55 + 8 ln 8 - 8 ln 3]

= (1/8) [55 + 8 ln(8/3)].

I hope this helps!

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