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Differential kinematic has a wide range application area in robot kinematics. The main advantage of the differential kinematic is that it can be easily implemented any kind of mechanisms. In differential kinematic method, Jacobian is used as a mapping operator in the velocity space. The joint velocities are required to be integrated to obtain the pose of the robot manipulator. This integration can be evaluated by using numerical integration methods, since the inverse kinematic equations are highly complex and nonlinear. Thus, the performances of the numerical integration methods affect the trajectory tracking application. This paper compares the performances of numerical integration methods in the trajectory tracking application of redundant robot manipulators. Four different and widely used numerical integration methods are implemented to the trajectory tracking application of the 7-DOF redundant robot manipulator named PA-10 and simulation results are given.