This question involves using a Matlab code (trapezoidal rule) from the textbook, Elementary Numerical Analysis. I need to code to work for the given problem below.

Here is the code straight from the textbook. Now I don't need those f_values, since my f(x) is (e^x)*cos(4x). Please help me figure this out, because Matlab is yelling at me and I don't understand why.

function [integral,difference,ratio]=trapezoidal(a,b,n0,index_f)

%Using the program for the trapezoidal rule given in the text, prepare a

%table of values of T_n(f) for n=2,4,8,...,512 for the following integrals.

%Also find the errors and the rations by which the errors decrease.

%

%n=n0,2*n0,4*n0,...,256n0,512*n0

%The value of n0 must be a positive integer.

%The corresponding numerical integrals are returned in the vector inegral.

%The difference of successive numerical integrals are returned in the

%vector difference:

% difference(i)=integral(i)-integral(i-1), i=2,...,10

%The entries of the ration given the rate od decrease in these differences.

%The parameter index_f allows the user to do calculations with multiple

%integrands.

%Initialize output vectors.

integral=zeros(10,1);

difference=zeros(10,1);

ratio=zeros(10,1);

%Intitialize for trapeziodal rule

sumend=(f(a,index_f)+f(b,index_f))/2;

sum=0;

%Intitialize for case of n0>2.

if(n0>2)

h=(b-a)0;

for i=2:2:n0-2

sum=sum+f(a+i*h,index_f);

end

end

%Calculate the numerical integrals, doing each by appropriately modifying

%the preceding case.

for i=1:10

n=n0*2^(i-1);

h=(b-a);

for k=1:2:n-1

sum=sum+f(a+k*h,index_f);

end

integral(i)=h*(sumend+sum);

end

%Calculate the differences of the successive trapezoidal rule integrals and

%the ratio of decrease in these differences.

difference(2:10)=integral(2:10)-integral(1:9);

ratio(3:10)=difference(2:9)./difference(3:10);

function f_value=f(x,index)

%This defines the integrand

switch index

case 1

f_value=exp(-x.^2);

case 2

f_value=1./(1+x.^2);

case 3

f_value=1./(2+cos(x));

end

2. Using the program for the trapezoidal rule given in the of prepare a text, table values of Tn(f) for n 2, 4, 8 512 for the following integrals. Also find the errors and the ratios by which the errors decrease n 2, 2. 2-512 e" 1 (a) e cos (4x) dx 17 2. Using the program for the trapezoidal rule given in the of prepare a text, table values of Tn(f) for n 2, 4, 8 512 for the following integrals. Also find the errors and the ratios by which the errors decrease n 2, 2. 2-512 e" 1 (a) e cos (4x) dx 17