A rocket of initial total mass \(M_0\) coasts at an initial speed \(v_0\) in deep space where all external gravitational and resistive forces are negligible. The rocket engines ignite, expelling propellant continuously backward at a constant speed \(u_{\text{rel}}\) relative to the rocket. Let \(m\) be the instantaneous mass of the rocket, such that the infinitesimal change in the rocket's mass during each time interval \(dt\) is \(dm < 0\). Which of the following integral expressions correctly gives the rocket's change in speed, \(\Delta v = v_f - v_0\), after its mass has decreased to a final value \(M_f\)?