Write a Matlab function, path Integral (P), which returns the result of the integral x +...

 

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Write a Matlab function, path Integral (P), which returns the result of the integral √x² + y² + z² dē The path P is expressed as a 3 x n array of points, where each column represents a single point along the path. You can assume the points are spaced closely enough to approximate the differential de. The function returns a 3D vector consisting of the x, y and z components of the resulting vector. 1. Calculate the integral analytically for the path (0,0,0)⇒(1,1,1), and compare the results with the output of your function. 2. Show how the accuracy of the integration changes as the path step size changes. 3. Provide other numerical examples of the output of your function, not necessarily accompanied by the exact analytical calculation. Write a Matlab function, path Integral (P), which returns the result of the integral √x² + y² + z² dē The path P is expressed as a 3 x n array of points, where each column represents a single point along the path. You can assume the points are spaced closely enough to approximate the differential de. The function returns a 3D vector consisting of the x, y and z components of the resulting vector. 1. Calculate the integral analytically for the path (0,0,0)⇒(1,1,1), and compare the results with the output of your function. 2. Show how the accuracy of the integration changes as the path step size changes. 3. Provide other numerical examples of the output of your function, not necessarily accompanied by the exact analytical calculation.

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