Computer-aided modeling and manufacturing, robotics and virtual reality applications require precise control of spatial position along a prescribed motion path. In several problems in these fields, it is preferable to maintain constant speed along the path. The shown path, defined betwen t = 0 and t = 1 is given by (x(t) = 0.5 + 0.3t+ 3.9t - 4.7t (y(t) = 1.5 + 0.3t+0.9t - 2.7t P = As seen, points defined by evenly spaced parameter values such as t = 0, 1/4, 1/2, 3/4 and 1 divide the path into non-equal partititons. The task is to apply numerical integration to determine the t values that will divide this path into N partitions of equal length. Recall from ME 210 that the arc length of the path from t to t is t = 1 t=0 t = 1/4 t = 1/2 t=3/4 [x'(t)]+ [y' (t)] dt Write a MATLAB code to partition the given path into N subpaths of equal length. In your code use MATLAB's built-in integral fuction for numerical integration. Explain the logic used in your code. Use your code for N = 4 and N = 10, and provide the obtained t values that separate each partition and the resulting partition lengths. :