I have written a small matlab function to compute the trapezoidal integration. The function takes the function to be integrated, the limits, and the number of strips to use, and it outputs the integration result for successive value of number of strips used up to the maximum.

For example, for this problem, I asked it to compute the integral for n=4, this is the result:

>> nStrips=4; f='x*exp(2*x)'; from=0; to=3; v=nma_trapezoidal(f,from,to,nStrips)

v =

1815.42957071731

952.907243435826

721.728546404322

630.878480889609

The last row in the result, is the asnwer for n=4.

This below is a run for n=20

>> nStrips=30; f='x*exp(2*x)'; from=0; to=3; v=nma_trapezoidal(f,from,to,nStrips)

v =

1815.42957071731

952.907243435826

721.728546404322

630.878480889609

586.718937655859

562.124445229887

547.079483006849

537.225888423362

530.429246311383

525.546941631965

521.923387644974

519.160963777893

517.00729763538

515.296023313487

513.913898807044

512.781695188809

511.842644620972

511.055216268612

510.388462738039

509.818943070872

509.328640480464

508.903523764667

508.532534744533

508.206863471385

507.919421428817

507.664453265978

507.437246953911

507.233914859052

507.051226580691

506.886480026577

function v=nma_trapezoidal(func,from,to,nStrips)

%function r=nma_trapezoidal(f,from,to,nStrips)

%

% integrates a function using trapezoidal rule

%

% INPUT:

% func : a string that repesents the function itself

% for example 'x*sin(x)'. The independent variable

% used in the string must be 'x' and no other letter.

%

% from: lower limit

% to : upper limit

% nStrips: number of strips to use

%

% OUTPUT

% v : a column vector that represents the trapeziodal

% intergation values. First row contains the

% value of integration when using 1 strip. second

% row for when using 2 strips, etc...

%

% Author: Nasser Abbasi

% May 3, 2003

v=zeros(nStrips,1);

for(j=1:nStrips)

nPoints=j+1;

X=linspace(from,to,nPoints);

h=X(2)-X(1);

f=zeros(length(X),1);

for(i=1:length(X))

x=X(i);

f(i)=eval(func);

end

sum=0;

for(i=1:length(X))

if(i==1 | i==length(X) )

sum=sum+f(i);

else

sum=sum+2*f(i);

end

end

sum=sum/2;

sum=sum*h;

v(j)=sum;

end