Question

In Matlab please

Given the function: So sin? (x)dx calculate the integral for all possible combinations of Simpson's 1/3 and Simpson's 3/8 rules for n=7, and then calculate the average of the values you obtained. Input your answer to 4 decimal places.

Answer 1

`Hey,

Note: If you have any queries related to the answer please do comment. I would be very happy to resolve all your queries.

clc

clear all

close all

format long

f=@(x) sin(x)^3;

I1=SimpsonComp(f,1,6,7);

I2=SimpThreeEight(f,1,6,7);

disp('Average is');

disp((I1+I2)/2)

function int=SimpsonComp(f,a,b,n)

%takes in parameter as function handel f, starting interval a and ending

%interval b for integration and number of intervals as n

h=(b-a)/n;%step of integration

fa=f(a);%value of function at a

fb=f(b);%value of function at b

ff=0;%initialize ff to 0

for i=2:2:n%traversing on even numbers i

x=(a+(i-1)*h);%accessing even points in the intervals divided

fx=feval(f,x);%value of function at x

ff=ff+4*fx;%add 4*fx to ff

end

for i=3:2:n%traversing on odd numbers i

x=(a+(i-1)*h);%accessing odd points in the intervals divided

fx=feval(f,x);%value of function at x

ff=ff+2*fx;%add 4*fx to ff

end

int=(h/3)*(fa+fb+ff);%finally add first and last points tto all the sum and divide by 3

end

function I = SimpThreeEight(f, a, b, n)

h = (b-a)/n;

S =feval(f,a);

for i = 1:3:n-2

x(i) = a + h*i;

S = S + 3*feval(f, x(i));

end

for i = 2:3:n-1

x(i) = a + h*i;

S = S + 3*feval(f, x(i));

end

for i = 3 : 3: n-3

x(i) = a + h*i;

S = S + 2*feval(f, x(i));

end

S = S + feval(f, b);

I = 3*h*S/8;

end

_ ww 26 end 27 int=(h/3)*(fa+fb+ff);%finally add first and last points tto all the sum and divide by 3 28 end 29 function I = Simp ThreeEight(f, a, b, n) 30 h = (b-a)/n; 31 S =feval(f, a); 32 - for i = 1:3:n-2 33 x(i) = a + h*i; 34 S = 5 + 3*feval(f, x(i)); 35 end 36 for i = 2:3:n-1 37 x(i) = a + h*i; 38 S = 5 + 3*feval(f, x(i)); 39 end 40 for i = 3: 3: n-3 41 x(i) = a + h*i; S = 5 + 2*feval(f, x(i)); 43 end 44 - S = S + feval(f, b); 45 - I = 3*h*S/8; 46 end Command Window New to MATLAB? See resources for Getting Started. Average is 0.001539831975629 O 42 х

Kindly revert for any queries

Thanks.