Simpson's 3 8 rule matlab

Problem Summar This example demonstrates using instructor-provided and randomized inputs to assess a function problem. Custom numerical tolerances are used to assess the output. Simpson's Rule approximates the definite integral of a function f(x) on the interval a,a according to the following formula + f (ati) This approximation is in general more accurate than the trapezoidal rule, which itself is more accurate than the leftright-hand rules. The increased accuracy of Simpson's rule is due to the fact that, while the trapezoidal rule approximates f as a linear function over an interval, Simpson's rule approximates f as a quadratic function, which leads to better results for smooth, nonlinear functions. In fact, it produces exact integral values for polynomials up to degree 3 By using Simpson's Rule over a sequence of n small, equally spaced subintervals and summing the results, we can approximate the definite integral of a function f over a larger interval [a, b] according to the formula: a + ai+ 2a) ai+1 ai where Δ= (which is constant with equal subinterval spacing) Your task is to complete the function I z simpson (f, a,b,n), which uses Simpson's method to approximate the definite integral value I of the input function f over the interval [a, b] using n subintervals. 1. Use the linspace function to create a vector x of n+1 equally spaced points 2. Define the value of Delta according to the formula above. You can use any two adjacent elements of x 3. Define the variable dI comesponding to value for the ith subinterval in the summand above 4. Set the range of values for the loop index i. These values will depend on your formula for dI When you have completed these tasks, call simpson using the test inputs provided and compare your results to the values given below. The absolute errors for both simpson and the trapezoidal method will be displayed for comparison. The first test uses a cubic function, for which Simpsons's method should returnthe exact value of 0.75 with no error . In the second test, your function should retum a value close to the true value of 1, with smaller eror than the trapezoidal method. Once your function returns reasonable values for the given test inputs, submit it for assessment.