Using Trapezoid and Simpson methods; write an m-file that plots and uses numerical integrations to estimate the following function y = x2 - 2x + 4 and its integral of y over the interval [0,30]. [10 marks] QUESTION 7 The velocity profile of a falling film is pg8? cos(B) Vz = (1-) 2 with the following constants: p = 800 g = 9.81 0 = 2.5 x 10-3 B = T1/4 u = 2.5 x 10-7. Calculate the volume flow per meter qm = S vzdx %3D with Simpson's rule (i.e.,for tol =1e^-6 and 1e^+2) and with the trapezoidal rule (i.e., if you take 5, 50 and 500 nodes in the interval (0,s)). Is any of these approximations actually the exact value? Why? [20 mark] QUESTION 8 8.1 What is Vectorization and why is it used? [4 marks] 8.2 Refine the below command in the vectorized form: [4 marks] A=[1:10)'; B=[1 26 9); D=zeros(length(A),1): for i=1:length(B) C=(A==B(1)); D=D+C; end