Please answer all the parts by showing the steps.

A group of chemical engineering students conducted an experiment to determine the concentration, X(T) of an antioxidant factor in an organic compound when the compound is subjected to heating and cooling. The following table gives a scaled representation of the data set obtained from the experiment. Here X(T) denotes the concentration of the antioxidant factor, and T denotes the temperature. (i) In order to find a Fourier series approximation for X(T) one student decided to numerically compute each Fourier coefficient by an approximated sum with the left end points. Write a program to compute the first 5 coefficients C0,C1,C2,C3 and C5 of the Fourier series, n=Cneint and find the Fourier series approximation for X(T) (ii) Another student decided to take a different approach to compute the coefficients, by assuming that the data set represents two linear pieces of functions l1 and l2 given by joining the two end points of the intervals [,0] and [0,] respectively. Compute the first five coefficients as in (i) and express the Fourier series. (iii) Compare the both ideas by computing the table values and graphing the both Fourier approximation curves, and conclude the best approach