A test vehicle of mass \(m\) is initially at rest at position \(x = 0\) on a horizontal, frictionless track. For the interval \(0 \le x \le L\), a propulsion system exerts a horizontal force on the vehicle given by \(F(x) = F_{\max} \sin\left(\dfrac{\pi x}{L}\right)\) in the \(+x\)-direction, where \(F_{\max}\) and \(L\) are positive constants. For \(x > L\), the propulsion system is deactivated and no horizontal forces act on the vehicle. Which of the following integral expressions correctly determines the maximum speed \(v_{\max}\) attained by the vehicle?