Question

Using Wolfram Mathematica 10.1

Implementing Simpson's Rule 3. Assume the values in exList are function values for an unknown function f(x), where the inputs are the whole numbers 1,2,3.,..., 9. So yl f(1), y2-f(2),..,.y9 f(9). Write some Mathematica code that uses Sum(] (probably more than once) to approximate fx)d x with Simpson's Rule, using 8 subinter- vals (so that Ax-1). Your output should be 4. Recall that we define a function with flx 1. Fill in the function definition below. It should output the Simpson's Rule approximation for the integral of a function whose values are given by the list pts, and Ax.It should work on any list with od length (which corresponds to an even number of subinter- vals) simpson (ptsAx 5. Test your code on the lists below to see if it works correctly.Assume Ax 2 in both cases. Note that the second list is the values of ysx,so your function approximates dx list1 (a, b, c, d, e, p, q, u,v) list2 (1, 9, 25, 49, 81) a, b, c, d, e,p,q,u,v (1, 9, 25, 49, 81) An Application: Income Inequality A big topic in the news today (and rightfully so) is income inequality. You often hear statistics like "the top 1% of Americans earn 20% of the income" and so forth. A basic tool for studying these issues is called the Lorenz Curve

Answer 1

Mathematica Thu May 23, 6:42 AM temp2-nb-Wolfram Mathematica 11.3 ile Fdit resert Format Cell Graphics Fgaluatien Palettes Windana Help, Question 3 nysimpson [a] (Print ["The value of the required integral is \n". +2+Sum [a[[i]], {i, {j, (1/3) * (a[[1]] 3, 7, 2}] 4*Sum [a[[j]], 2, 8, 2}] a[[9])))) :. 叩 : n3 nysimpson[y] The value of the requtred 1ntceral 1s Question 4 simpson[pts, deltax 1 Print [ "The value of (1- Length[pts]; the required integral . 4.Sum[ptstn,.. . pt,a,n)/ is \n" , (deltax /3). (pts([1)j . 2. Sum[ptsllil, ti, 3, 1-2, 21 , Question 5 ng Clear [ali sti-(a, b,, d, e, p, q,u, v) us a, b, c,d, e, P q, U, v) lel-simpson[listl, 2] The value of the required 1ntegral 1s - List2-(1, 9, 25, 49, 81) u7 (1, 9, 25, 49, 81 ro simpson [list2, 2] The value of the required integral is 728 125%