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Find the exact length of the curve analytically by antidifferentiation. You will need to simplify the integrand algebraically before finding an antiderivative.

1. y = (1/3)(x^2 + 2)^(3/2), from x = 0 to x = 3

and

2. x = (y^3)/3 + 1/(4y), from y = 1 to y = 3
[HINT: 1 + (dx/dy)^2 is a perfect square]

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