Question

Question:

Code your own MATLAB program to find the approximate value of the

Integeral 0 to 2 e^x dx with Trapezoidal rule for N = 20, i.e., t20. Also give the relative error of t₂₀ with

Integeral 0 to 2 e^x dx = e² − 1.

(Hint: For-end loops or Elementwise operations)

Answer 1

To calculate the integration we shall use the trapezoidal rule given below:

%%%SCRIPT STARTS%%%

upperLimit = 2;
lowerLimit = 0;
N = 20;
h = (upperLimit - lowerLimit) / N;

y = []; % will store values of function at differnt points
for i = lowerLimit:h:upperLimit
    y = [y, exp(i)];
end
%Trapezoidal rule starts
sum = y(1) + y(length(y)); %add first and last element

for i = 2:length(y)-1
    sum = sum + 2*y(i); %add remaining items multiplied by 2
end

results = sum * h / 2 %get results

actualResult = exp(2) - 1;%get actual result of the integration

absoluteError = abs(results - actualResult); %absolute error
relativeError = absoluteError/actualResult %calculate relative error

I tried to keep the code as simple as possible. I have also commented almost every line of the code to make things easy. If incae you face trouble with the code, please feel free to comment below. I shall be glad to help you :)