solve with MATLAB. Programming Part: For each programming problem, please submit

Question

solve with MATLAB.

Programming Part: For each programming problem, please submit the code and the output by pasting them into a word document and attaching them to your homework. 1. (7.2 1d) Write a numerical code (or use the textbook code) that implements Composite Trapezoid and Composite Simpson Rule. Apply this code to approximate the integral J edz for (a) Composite Trapezoid for M = 10 and (b) Composite Simpson for M = 5·Which produces less error? (Hint: You can integrate by parts twice to find the exact answer).

Explanation / Answer

function simps(a, b, n)

h = (b-a)/n;

sum0 = 0;

for i = 1:n/2-1

x(i) = a + 2*i*h;

sum0 = sum0 + f(x(i));

end

sum1 = 0;

for i = 1:n/2

x(i) = a + (2*i-1)*h;

sum1 = sum1 + f(x(i));

end

integral = h*(f(a)+ 2*sum0 + 4*sum1 +f(b))/3

function y = f(x)

y = (x^2)*exp(-x);

function trapez(a, b, n)

h = (b-a)/n;

sum = 0;

for i = 1:n-1

x(i) = a + i*h;

sum = sum + f(x(i));

end

integral = h*(f(a) + 2*sum + f(b))/2

function y = f(x)

y = (x^2)*exp(-x);

Outputs

Trapezoidal = 1.52163

Simpson =1.523793

Exact Ans = 1.523793

Simpsons rule gives less error

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