Code adaptive refinement for the Rectangle, Trapezium and Simpson's Rules, where the number of intervals in x and y directions are progressively increased from 8 to 80 in steps of 2. The following types of refinement should be implemented for each rule: a. Onlv increase the number of intervals in the x direction in steps of 2, leaving the number of intervals in the y direction constant at 8. b. Only increase the number of intervals in the y direction in steps of 2, leaving the number of intervals in the x direction constant at 8. Simultaneously increase the number of intervals in the x and y direction from 8 to 80 in steps of 2. Show your Matlab code.

Please answer using this template

close all; clearvars; clc;

%define integration method

sel_meth = -1;

disp('Integration Method:');

disp('1) Rectangular, 2) Trapezium, 3) Simpsons 4) Gaussian');

%ensure that correct number is provided

while (sel_meth~=1 && sel_meth~=2 && sel_meth ~=3 && sel_meth ~=4 )

sel_meth = input('Please Select integration method: 1,2,3 or 4 ');

end

N = -1;

disp('Set Number of intervals in x direction, or of Gauss points:');

while (N<1 || uint8(N)~=N ) % so N has to be < 255 (2^8=256-> max unsigned 8-bit integer : 255)

N = input('Please provide a positive integer ');

end

M = -1;

disp('Set Number of intervals in y direction, or of Gauss points:');

while (M<1 ||uint8(M)~=M ) % also M <255

M = input('Please provide a positive integer ');

end

x_min=inf; y_min=inf;

disp('Set the lower limits for integration:');

while (isinf(x_min) && isnumeric(x_min))

x_min = input('In the x direction: ');

end

while (isinf(y_min) && isnumeric(y_min))

y_min = input('In the y direction: ');

end

x_max=-inf; y_max=-inf;

disp('Set the upper limits for integration:');

while (isinf(x_max) && isnumeric(x_max) && (x_max

x_max = input('In the x direction: ');

end

while (isinf(y_max) && isnumeric(y_max) && (y_max

y_max = input('In the y direction: ');

end

%x_min=-1; x_max=0; y_min=0; y_max=2;

switch sel_meth

case 1

INTEGRAL=Rect_2D_tut_analytic(@fun1,x_min,x_max,y_min,y_max,N,M);

METHOD= 'Rectangle';

case 2

INTEGRAL=Trap_2D_tut_analytic(@fun1,x_min,x_max,y_min,y_max,N,M);

METHOD = 'Trapezium';

case 3

INTEGRAL=simp_2D_tut_analytic(@fun1,x_min,x_max,y_min,y_max,N,M);

METHOD = 'Simpsons';

case 4

INTEGRAL=Gauss_2D_tut_analytic(@fun1,x_min,x_max,y_min,y_max,N,M);

METHOD = 'Gauss';

end