Matlab/c++ programming question

[Rachelross]

Matlab/c++ programming question please help:)

Homework Statement

Look up Simpson’s Rule and explore the effect on this integration method of
changing the strip size on the error. Also, explore the effect of changing the strip size
in the left-hand and right-hand rules for integration. Compare the convergence of the
integral as the strip size decreases for all four integration methods

Homework Equations

Simpson's rule
The integration formula I =∫f (x) dx (The interval is from a to b)
The integration approximation formula I ≈ Δx( (y0 + yn )/2+ Σ yi)

The Attempt at a Solution

Okay I do not want a solution but maybe some hints as I have no idea how to start this program

 

[Valkarie]

. For the Simpson's rule, you can use a numerical integration technique that is based on the trapezoid rule. The trapezoid rule is a way of approximating the area under a curve by dividing it up into sections or "strips" and calculating the area of each strip. You can then calculate the total area under the curve by summing up the areas of all the strips. Simpson's rule improves upon the trapezoid rule by using a polynomial function to approximate the area. In Simpson's rule, the area of each strip is calculated using a third-order polynomial instead of the linear function used in the trapezoid rule. In order to explore the effect of changing the strip size on the error, you can calculate the error for each strip size. To do this, you will need to calculate the exact integral value for comparison and then compare this to the value obtained from Simpson's rule. You can then calculate the error for each strip size and plot the results to see how the error changes as the strip size decreases. To explore the effect of changing the strip size in the left-hand and right-hand rules for integration, you can again calculate the exact integral value for comparison and then compare this to the values obtained from the left-hand and right-hand rules. Again, you can calculate the error for each strip size and plot the results to see how the error changes as the strip size decreases. Finally, you can compare the convergence of the integral as the strip size decreases for all four integration methods by plotting the errors for each method and comparing the results.