Xét tích phân \(I = \int\limits_0^{\frac{\pi }{2}} {\frac{{\sin 2x}}{{\sqrt {1 + \cos x} }}} \,dx\).

A. \(I = \int\limits_1^{\frac{\pi }{2}} {\frac{{4{t^3} - 4t}}{t}} \,dt\)

B. \(I =  - 4\int\limits_1^{\sqrt 2 } {\left( {{t^2} - 1} \right)} \,dt\)

C. \(I = \int\limits_{\sqrt 2 }^1 {\frac{{ - 4{t^3} - 4t}}{t}} \,dt\)

D. \(I = 4\int\limits_1^{\sqrt 2 } {\left( {{t^2} - 1} \right)} \,dt\)