MATLAB trapz function error

Question

I am working on an assignment that requires me to use the trapz function in MATLAB in order to evaluate an integral. I believe I have written the code correctly, but the program returns answers that are wildly incorrect. I am attempting to find the integral of e^(-x^2) from 0 to 1.

x = linspace(0,1,2000);
y = zeros(1,2000);
for iCnt = 1:2000
    y(iCnt) = e.^(-(x(iCnt)^2));
end

a = trapz(y);
disp(a);

This code currently returns

1.4929e+03

What am I doing incorrectly?

Answer 1

You need to just specify also the x values:

x = linspace(0,1,2000);
y = exp(-x.^2);
a = trapz(x,y)

a =

    0.7468

More details:

• First of all, in MATLAB you can use vectors to avoid for-loops for performing operation on arrays (vectors). So the whole four lines of code

  y = zeros(1,2000); for iCnt = 1:2000 y(iCnt) = exp(-(x(iCnt)^2)); end

will be translated to one line:

y = exp(-x.^2)

• You defined x = linspace(0,1,2000) it means that you need to calculate the integral of the given function in range [0 1]. So there is a mistake in the way you calculate y which returns it to be in range [1 2000] and that is why you got the big number as the result.

• In addition, in MATLAB you should use exp there is not function as e in MATLAB.

• Also, if you plot the function in the range, you will see that the result makes sense because the whole page has an area of 1x1.