find the length of the curve y=1/3 (x^2+2)^3/2 from x=0 to x=3

Question

L=integral a to b root of 1+ (dy/dx)^2.

Answer 1

The curve equation is y = 3x^3/2 - 1 and the interval is [0, 3].

The arc length of f(x) between a and b is

y = (1/3)(x²+2)^3/2 ⇒ y' = (1/3)(3/2)(2x)(x²+2)^1/2 ⇒ y' = x(x²+2)^1/2.

Substitute y' = x(x²+2)^1/2, a = 0 and b = 3 in the above formula.

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