How can use Simpsons rule to write a matlab code or java cod

How can use Simpson\'s rule to write a matlab code or java code for below question?

Question:

Find the area when n = 2. I wrote below code by matlab, but I think it is not completely correct.Can you find problem for me ?

f=@(x)(x*sin(x)^2)

format long

a=0

b=3

n=2

dx=(b-a)/n

sum_even = 0;

for i = 1:n/2-1

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

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

end

sum_odd = 0;

for i = 1:n/2

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

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

end

A = dx*(f(a)+ 2*sum_even + 4*sum_odd +f(b))/3

******************************

A=3.01486102991289 (I believe this is wrong)

//A tutor said my code is correct expect the last A equation but he did not said any specific error.//

Solution

Ex-2: solve the equation .

     Method -1: =?

>> f=inline(\'x.^2\')

f =     Inline function:

     f(x) = x.^2

>> Q=quad(f,0,2)

Q =    2.6667

Method -2:

=?

>> f=@(x) x.^2    % ‘.^’ term-by-term exponentiation.

f =     @(x)x.^2

>> Q=quad(f,0,2)

Q =    2.6667

Method -3:          =?

>> syms x

>> f=x.^2

f = x^2

>> Q=int(f,0,2)

Q = 8/3

Method -4:

>> int(sym(\'x^2\'),0,2)

ans = 8/3

>> eval(ans)

ans =    2.6667

Ex-3: simply the following function

=?

Method -1:

>> f=inline(\'sin(x)\')

f =     Inline function:

     f(x) = sin(x)

>> Q=quad(f,0,5)

Q =    0.7163

Method -2:

>> f=@(x) sin(x)

f =     @(x)sin(x)

>> Q=quad(f,0,5)

Q =    0.7163

Method -3:

>> int(sym(\'sin(x)\'),0,5)

ans = 1 - cos(5)

>> eval(ans)

ans =    0.7163

Ex-4 :   =?

Method -1:

>> int(sym(\'sqrt(x)\'),0,2)

ans = (4*2^(1/2))/3

>> eval(ans)

ans =    1.8856

Method -2:

>> f=inline(\'sqrt(x)\')

f =    Inline function:

     f(x) = sqrt(x)

>> quad(f,0,2)

ans =    1.8856

Method -3:

>> f=@(x) sqrt(x)

f =    @(x)sqrt(x)

>> quad(f,0,2)

ans =    1.8856

Ex-5:

5. =?

Method -1:

>> sym x

ans =x

>> f=(\'sqrt(x.^2-(sin(x)).^4)\')

f = sqrt(x.^2-(sin(x)).^4)

>> Q=quad(f,0,2)

Q =    1.5824

Method -2:

>> f=(\'sqrt(x.^2-(sin(x)).^4)\')

f = sqrt(x.^2-(sin(x)).^4)

>> quad(f,0,2)

ans =    1.5824

Method -3:

>> f=@(x) sqrt(x.^2-(sin(x)).^4)

f =     @(x)sqrt(x.^2-(sin(x)).^4)

>> quad(f,0,2)

ans =    1.5824

Method -4:

>> f=inline(\'sqrt(x.^2-(sin(x)).^4)\')

f =

     Inline function:

     f(x) = sqrt(x.^2-(sin(x)).^4)

>> Q=quad(f,0,2)

Q =    1.5824

Method -5:

6. Evaluate .

Method -1:

>> syms x

>> f=(cos(x))^6

f =cos(x)^6

>> int(f,0,pi/2)

ans =(5*pi)/32

>> eval(ans)

ans =    0.4909

Method -2:

>> syms x

>> f=@(x) (cos(x)).^6

f =     @(x)(cos(x)).^6

>> Q=quad(f,0,pi/2)

Q =    0.4909

Method -3:

>> syms x

>> f=inline(\'(cos(x)).^6\')

f =     Inline function:

     f(x) = (cos(x)).^6

>> Q=quad(f,0,pi/2)

Q =    0.4909

Method -4:

>> f=@(x) (cos(x)).^6

f =     @(x)(cos(x)).^6

>> Q=quad(f,0,pi/2)

Q =    0.4909

7. Evaluate

Method -1:

>> f=(sin(x))^2*(cos(x))^2

f =   cos(x)^2*sin(x)^2

>> int(f)

ans = x/8 - (cos(x)*sin(x))/8 + (cos(x)*sin(x)^3)/4