romberg function :

function [q,ea,iter]=romberg(f,a,b,es,maxIt)

% romberg: Romberg integration quadrature

% q = romberg(f,a,b,es,maxIt): Romberg Integration

%

% inputs:

% f = function to integrate

% a, b = integration limits

% es = desired relative error (default = .000001%)

% maxIt = maximum allowable iterations (default=50)

% outputs:

% q = integral estimate

% ea = approximate relative error

% iter = number of iterations

if nargin

if nargin

if nargin

I(1,1) = trap(f,a,b,1);

iter = 0;

while iter

iter = iter+1;

n = 2^iter;

I(iter+1,1) = trap(f,a,b,n);

for k = 2: iter+1

j = 2+iter-k;

I(j,k) = (4^(k-1)*I(j+1,k-1)-I(j,k-1)) /(4^(k-1)-1);

end

ea = abs((I(1,iter+1)-I(2,iter))/I(1,iter+1))*100;

if ea

end

q = I(1,iter+1);

end

oConsider the function given in problem 1 over the interval from 0 to 1 (a) Use the Romberg integration technique to calculate the integral with an error of o(h8) Using Matlab Show all of the steps. You can use the trap function but not the romberg function. Print the results in a table like the one below 4X. xxXXxXXXXx (b) Use the romberg function with default tolerance and maximum iterations to verify your answer. Use an appropriate fprintf statement to print the result with 10 digits after the decimal point. (c) Why is the error not zero for the Gauss-Legendre method? Use an fprintf statement to print your answer. oConsider the function given in problem 1 over the interval from 0 to 1 (a) Use the Romberg integration technique to calculate the integral with an error of o(h8) Using Matlab Show all of the steps. You can use the trap function but not the romberg function. Print the results in a table like the one below 4X. xxXXxXXXXx (b) Use the romberg function with default tolerance and maximum iterations to verify your answer. Use an appropriate fprintf statement to print the result with 10 digits after the decimal point. (c) Why is the error not zero for the Gauss-Legendre method? Use an fprintf statement to print your