Find the length of the curve y1279x2632 from x0 to x6Solutio

Find the length of the curve y=1/27(9x^2+6)^3/2 from x=0 to x=6

y = (9x² + 6)^3/2/27

y\' = x(9x² + 6)^1/2

1 + y\'² = 1 + x²(9x² + 6) = (3x² + 1)²

(1 + y\'²) = 3x² + 1

arc length = ₀⁶ (1 + y\'²) = ₀⁶ (3x² + 1) dx = x³ + x |₀⁶ = 222

$Find the length of the curve y=1/27(9x^2+6)^3/2 from x=0 to x=6Solutiony = (9x2 + 6)3/2/27 y\' = x(9x2 + 6)1/2 1 + y\'2 = 1 + x2(9x2 + 6) = (3x2 + 1)2 (1 + y\'2$

Find the length of the curve y1279x2632 from x0 to x6Solutio

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