Question

Throughout this homework, rz)-e-5s sin 릎 sin siIT, unless stated otherwise. Q1 The Boole's quadrature rule is Use the midpoint, trapezoid (by hand & a calculator). Sinnp ons and Bole's rule (MATLAB), respectively, to approximate If = / f(x)dx, where a-0.19 and b 0.29. Compare with exact I0. errors. 2115910278025609 and show the

Answer 1

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clc
clear all
f=@(x) exp(-5*x)*sin(1/x)*sin(1/sin(1/x));
a=0.19;
b=0.29;
If=0.02115910278025609;
n=5;
disp('Mid point inegral is');
I=0;
h=(b-a)/n;
for i=1:n
I=I+h*f(a+(2*i-1)*h/2);
end
disp(I)
disp('Error is');
abs(I-If)
disp('Trapezoidal inegral is');
I=trapezoid(f,a,b,n)
disp('Error is');
abs(I-If)
disp('Simpson inegral is');
I=SimpsonComp(f,a,b,n)
disp('Error is');
abs(I-If)
disp('Boole inegral is');
I=(b-a)/90*(7*f(a)+32*f((3*a+b)/4)+12*f((a+b)/2)+32*f((a+3*b)/4)+7*f(b))
disp('Error is');
abs(I-If)

function I = trapezoid(func,a,b,n)

% I = trap(func,a,b,n):

% multiple-application trapezoidal rule.

% input:

% func = name of function to be integrated

% a, b = integration limits

% n = number of segments

% output:

% I = integral estimate

x = a;

h = (b - a)/n;

s = feval(func,a);

for i = 1 : n-1

x = x + h;

s = s + 2*feval(func,x);

end

s = s + feval(func,b);

I = (b - a) * s/(2*n);
end

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

MATLAB R2018a EDITOR Search Documentation Log In Find Files Compare ▼ Print Run Section New Open Save Advance Run and Find Indent Advance Time C: Users PRADEEP KALRA 、Documents MATLAB Current Folder Editor-CNUsersPRADEEP KALRAD Name- Newton!·m × m secantbypradeep.m xlnewtonrapsonsbypradeep.m ×1+ E mathlab | function tx,ta,k1-Ne E (x) exp (-0.5*x) *cos (5*x)-0.5 3a(x)-cos (5 x) exp (-x/2))/2 4-1 e-5 keps ; 5-1 maxit=1000; 6-x1-x0: 5*sin (5 x) exp-x/2) New folder a1.m x0=0 ; a4.m a5.m A1.dat A1.mat A2.dat A3.dat 4.dat Command Window New to MATLAB? See resources for Getting Started [x, Is,k]-Newtonl(O) Details 1.164097002443509 Name ▲ Value x1 sym 1.6653e-16 fs -1.665334536937735e-16 1.1641 x12 double x12 double x12 double y1 fx >> ENG 902 AM O Type here to search

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