Calculate following integral, b=6 | (x* cosx – 2)dx = 435.81767401 a=2 by following methods. (Consider in each case, number of points n contains initial (a) and end points (b). Also, points are selected as equidistantly.) a) Trapezoidal rule. i) n = 5. (Solve by hand and give analytical expressions explicitly) ii) ) Write computer code performing integration by trapezoidal rule. Perform the calculation for n = 2k; k = 1,2, ...,10. Obtain a table containing n, In, In - lexactl where In is calculated integral for n point, and lexact is exact value of the integral given in the question. b) Simpson's 1/3 rule. i) n = 5. (Solve by hand and give analytical expressions explicitly) (10p) ii) Write computer code performing integration by Simpson's 1/3 rule. Perform the calculation for n = 2k + 1; k = 1,2, ...,10. Obtain a table containing n, In, In - lexact! where In is calculated integral for n point, and lexact is exact value of the integral given in the question. c) Simpson's 3/8 rule. i) n = 7. (Solve by hand and give analytical expressions explicitly) (10p) ii) ) Write computer code performing integration by Simpson's 3/8 rule. Perform the calculation for n=3(2k-1) + 1; k = 1,2,...,10. Obtain a table containing n, In, \In – lexactwhere In is calculated integral for n point, and lexact is exact value of the integral given in the question.