Question

4. This question is about using the composite Simpson's Rule to estimate the integral 1 = (exp() dr to ten decimal places. (a) Enter and save the following Matlab function function y = f(x) y =exp(x/2); end [O marks) (b) Now complete the following Matlab function function y = compSR (a,b,N) end The function is to return the estimate of I found by applying Simpson's Rule N times. The Matlab function from the previous part of the question should be called each time compSR needs to evaluate the integrand. (5 marks] (c) Estimate I by applying the composite Simpson's rule with h=2-, i = 1,2,.... Keep halving h and re-estimating I until you have a sufficiently accurate answer or you can not get any more accuracy. 15 marks)

Answer 1

`Hey,

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

clc
clear all
close all
format long
n=2;
a=-2;
b=2;
while(1)
I=CompSR(a,b,n);
if(abs(I-2*exp(-1)*(exp(2) - 1))<0.5e-10)
break;
end
n=2*n;
end
fprintf('Approximation is %.10f\n',I);

function int=CompSR(a,b,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=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=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 y=f(x)
y=exp(x/2);
end

MATLAB R2018a X Pradeep EDITOR VIEW Search Documentation НOME PLOTS APPS PUBLISH Find Files fxF Insert Run Section Г Comment % SGo To FCompare Run and E Advance New Open Save Breakpoints Run Run and Indent Time Print QFind Advance FILE NAVIGATE EDIT BREAKPOINTS RUN C: Windows System32 Editor - C:\Users\PRADEEP KALRA\Documents\MATLAB\saveee.m Current Folder X xgoogleLinks.m HomeworkLib1.m HomeworkLib2.m X testc.m eulerSystem.m ahk.m bisectionmethodbypradeep.m + Name saveee.m 0409 fa-f (a);value of function at a fb=f (b) value of function at b ff-0 initialize ff to 0 Efor i-2:2:nstraversing on even numbers i 18 1029 19 1033 + 20 1036 + 21 1040 X= (a+(i-1) *h);%accessing even points in the intervals divided 22 1045 23 fx-f (x) value of function at 1046 + ff-ff+4*fx; %add 4*fx to ff 24 1049 end 25 F 1055 + for i-3:2 : n%traversing on odd numbers 26 3082 X=(a+(i-1) *h) ; %accessing odd points in the intervals divided fx-f(x) value of function at 27 AdvancedInstallers + 28 af-ZA ff-ff+2*fx; %add 4*fx to ff 29 am-et + 30 end AppLocker int= (h/3) * (fa+fb+ff);%finally add first and last points tto all the sum and divide by 31 appraiser 32- end Efunction Details y f (x) 33 Workspace у-ехp (x/2); 34 end Name Value 35 -2 a Command Window 2 b New to MATLAB? See resources for Getting Started. 4.7008 512 n Approximation is 4.7008047746 fax>> CompSR/f Ln 35 Col 4 ENG 2:07 PM OType here to search US 10/16/19

Kindly revert for any queries

Thanks.