How does additional error affect integration? Try it and see, using the same random error term you used before.

As an AI, I'm unable to directly perform computations. However, I can guide you on how to do it.

1. Choose a function for which you know the integral. For example, let's take f(x) = sin(x). The integral of this function is F(x) = -cos(x) + C, where C is the constant of integration.

2. Add some additional error to your function. In MATLAB, you can use the randn function to generate random numbers. For example, y = f(x) + 0.001 * randn(size(x));. This will add a small random error to your function.

3. Choose different step sizes h. For example, you can choose h = 1, 0.1, 0.01, 0.001, etc.

4. Calculate the numerical integrals at x = 0, 1, 1.5, and 2 using a numerical integration method, such as the trapezoidal rule or Simpson's rule.

   Trapezoidal rule: ∫f(x)dx ≈ h/2 * (f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(xn)) Simpson's rule: ∫f(x)dx ≈ h/3 * (f(x0) + 4f(x1) + 2f(x2) + ... + 4f(xn-1) + f(xn))

5. Calculate the actual integral at x = 0, 1, 1.5, and 2 using the integral function F(x) = -cos(x) + C.

6. Calculate the error at each x for each step size h. The error is the absolute difference between the numerical integral and the actual integral.

7. From the errors, you can see how the additional error affects the numerical integration.

Remember, the accuracy of the numerical integration depends on the step size h. The smaller the step size, the more accurate the numerical integration. However, if the step size is too small, you may encounter round-off errors. The added error will likely increase the overall error in the numerical integration.