Write a function trap fabn that computes the trapezoidal rul

Write a function trap (f,a,b,n) that computes the trapezoidal rule approximation to f(x) dx, where h = (b - a)/n and xi = a + ih. Test your function on sin(x) + cos(x) for 0 x pi/3. For a greater challenge, write a function simp for Simpson\'s rule, This formula requires n to be even. You may choose to check the input for this

Solution

function integral = trap(a,b,n,f)

h = (b-a)/n;

x = [a+h:h:b-h];

integral = h/2*(2*sum(feval(f,x))+feval(f,a)+feval(f,b));

function y = f(t)

y = t.*log(t);

. Matlab code for the Simpson’s rule

function integral = simp(a,b,n,f)

h = (b-a)/n;

xi0 = feval(\'f\',a)+feval(\'f\',b);

xi1 = 0;

xi2 = 0;

for i = 1:n-1

x = a+i*h;

if mod(i,2) == 0

xi2 = xi2+feval(\'f\',x);

else

xi1 = xi1+feval(\'f\',x);

end

end

xi = h*(xi0+2*xi2+4*xi1)/3;

x