Since dy/dx = 2√2 x^(1/2), the arc length equals
∫(x = 0 to 1) √[1 + (2√2 x^(1/2))^2] dx
= ∫(x = 0 to 1) (1 + 8x)^(1/2) dx
= (1/8)(2/3)(1 + 8x)^(3/2) {for x = 0 to 1}
= (1/12)(27 - 1)
= 13/6.
I hope this helps!
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Verified answer
Since dy/dx = 2√2 x^(1/2), the arc length equals
∫(x = 0 to 1) √[1 + (2√2 x^(1/2))^2] dx
= ∫(x = 0 to 1) (1 + 8x)^(1/2) dx
= (1/8)(2/3)(1 + 8x)^(3/2) {for x = 0 to 1}
= (1/12)(27 - 1)
= 13/6.
I hope this helps!