Write and simplify an integral with respect to x that gives the length of the curve y=2cos4x on the interval -(π)/(3),(π)/(4). Which of the following options correctly represents the integral?

A) ∫(π)/(4) -(π)/(3) √(1+(2sin4x)2) dx
B) ∫(π)/(4) -(π)/(3) √(1+(8cos4x)2) dx
C) ∫(π)/(4) -(π)/(3) √(1+(2cos4x)2) dx
D) ∫(π)/(4) -(π)/(3) √(1+(8sin4x)2) dx