A boat of mass \(m\) glides across the surface of a calm lake with an initial speed \(v_0\). At time \(t = 0\), the engine is shut off, and the water exerts a net resistive force of magnitude \(F_R = bv + cv^2\) on the boat, where \(b\) and \(c\) are positive constants and \(v\) is the instantaneous speed. Which of the following integral expressions correctly gives the elapsed time \(T\) required for the boat's speed to decrease to \(\dfrac{1}{2}v_0\)?