The length of a curve or arc length is equal to this definite integral:
[tex]arc length= \int\limits^a_b {} \, ds [/tex]
Where
[tex]ds= { \sqrt{1+ ( \frac{dy}{dx} )^{2} } }dx[/tex]
The curve seems to be [tex]y= 4x^{3/2} [/tex]
These are the calculations step by step:
1) dy/dx = 4*(3/2)x^(1/2) = 6x^(1/2)
2) length = ds = √ (1+ [6x^(1/2)]^2 ) dx = √ (1 + 36x)dx
3) ∫ds from a to b = ∫ √(1 + 36x) dx from a to b =
= (1/54) (1 + 36x)^(3/2) from a to b
a 0 and b = 1 => lentgh = (1/54) (1 + 36)^(3/2) - (1/54) (1)
=> length = 4.15
Answer: 4.15
