A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \[{\text{y}} = 4{\text{h}}\left( {\frac{{{{\text{x}}^2}}}{{{{\text{L}}^2}}}} \right)\]  , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

A. \[\int\limits_0^{\text{L}} {\sqrt {1 + 64\frac{{{{\text{h}}^2}{{\text{x}}^2}}}{{{{\text{L}}^4}}}} } {\text{dx}}\]

B. \[2\int\limits_0^{\frac{{\text{L}}}{2}} {\sqrt {1 + 64\frac{{{{\text{h}}^3}{{\text{x}}^2}}}{{{{\text{L}}^4}}}} } {\text{dx}}\]

C. \[\int\limits_0^{\frac{{\text{L}}}{2}} {\sqrt {1 + 64\frac{{{{\text{h}}^2}{{\text{x}}^2}}}{{{{\text{L}}^4}}}} } {\text{dx}}\]

D. \[2\int\limits_0^{\frac{{\text{L}}}{2}} {\sqrt {1 + 64\frac{{{{\text{h}}^2}{{\text{x}}^2}}}{{{{\text{L}}^4}}}} } {\text{dx}}\]

Answer: Option D