Find the arc length of the graph of the function over the indicated interval.

Question

x=1/3(y² + 2)^3/2,    0 ≤ y ≤ 8

Answer 1

Length of arc s = ∫₀⁸(1 + (dx/dy)²)^1/2dy = ∫₀⁸(1 + y²(y² + 2))^1/2dy = ∫₀⁸(y⁴ + 2y² + 1)^1/2dy = ∫₀⁸(y² + 1)dy =

(y³/3 +, y)₀⁸ = 512/3 + 8 = 536/3