Question

(a) (4 points) Fill in the blanks in the following MATLAB function M file trap so that it implements the composilu trapezidul rulo, using a soquence of w -1,2, 4, 8, 16,... trapezoids, to approximatel d . This M file uses the MATLAB built-in function trapz. If 401) and y=() f(!)..... fr. 1)). 3= ($1, then the execution of z = trapz(x, y) approximates using the composite trapezoidal rule (with trapezoids). (Note that the entries of are labeled starting at 2 because MATLAB does not allow an index of 0.) The function M-file trap has 4 input parameters: • u and the lower and upper limits of the interal); • zaxiter (tlac maximum number of iterations that are allowed the above program will implement the composite trapezoidal rule with a sequence of 1, 2, 4, 8, 16,... trapezoids, up to a maximum of 2 st. trapezoids): • tol (a tolerance for testing the relative error of the computed approximation). Tf the difference between 2 successive approximations with respect to relative error) is tol, then the algorithm terminates. You also must delincul storca MATLAB (uncliou M-lile y = f(x) which must be written to accept a vector x as the argument. Nolo that this means that you muslu arithcli operators like .:., ./ und , ratlar jul, function trap(a, b, maxiter, tol) I = linapace(a, b, +1); y = f(x); appror = trapz(x, y); disp(' m integral approximation'); fprintf(! %5.0 X16.10f \n', m, approx); for i = 1 : maxiter oldapprox = ---------- I =linspace - -- -- -- ---- y = f(x); approx = trapz(x, y); fprintf(%5.0f %16.10f \n', ., approx); if aba -------) <tol return end ond fprintf('Did not converge in lg iterations'. saxiter) DELIVERABLES: A copy of your function trap. Feel free to wel aan extra arameter fut the end of rameter list to make your function walls simpler. (4 points) Use the above MATLAB script to approximate the following two integrals: scos(1/1)dt using maxiter = 20 and tol = 10- sin(v1+1+1)dr using maxiter = 20 and tol = 10 ! DELIVERABLES: The MATLAB calls and cutput for each. If you 1: function files tax evalutach of the functions I also want them files for those

Answer 1

`Hey,

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clc%clears screen
clear all%clears history
close all%closes all files
format long
disp('part a & b (i)');
trap(0.1,3,20,1e-5)

function trap(a,b,maxiter,tol)
m=1;
x=linspace(a,b,m+1);
y=f(x);
approx=trapz(x,y);
disp('m integral approximation');
fprintf(' %5.0f %16.10f \n',m,approx);
for i=1:maxiter
m=2^i;
oldapprox=approx;
x=linspace(a,b,m+1);
y=f(x);
approx=trapz(x,y);
fprintf(' %5.0f %16.10f \n',m,approx);
if(abs((approx-oldapprox)/approx)<tol)
return;
end
  
end
fprintf('Did not converge in %g iterations\n',maxiter);
end

function y=f(x)
y=x.*cos(1./x);
end

- O X Pradeep EDITOR PUBLISH VIEW do E C . Search Documentation Insert fx Comment % 92% & Indent 1 - EDIT Run Section El Advance Breakpoints EL Run and Advance Run Aduan Run and Time BREAKPOINTS RUN O ох googleLinks.m x HomeworkLib2.m x testcm x ahk.m x nse_filt.m x + | MATLAB R2018a HOME PLOTS APPS D E L Find Files 3 Compare - New Open Go To - Save Print Find FILE NAVIGATE a Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Editor - C:\Users\PRADEEP KALRA\Documents\MATLAB\saveee.m +1 saveee. m x bisectionmethodbypradeep.m x eulerSystem. m x y=f(x): approx=trapz (x,y); fprintf(' $5.0f $16.10f \n',m, approx); if (abs ((approx-oldapprox) /approx) (tol) return; end end fprintf("Did not converge in Sg iterations\n', maxiter); Lend function y=f(x) y=x.*cos(1./x); Lend 30 - © Details Workspace Name Value Command Window m integral approximation 3.9888973448 3.7902074408 3.5976493493 3.4808457876 3.4678411685 3.4856113710 3.4877924488 128 3.4870325249 256 3.4867926880 512 3.4867333190 1024 3.4867185769 trap/f In 30 col 4 Type here to search IN 03/31/20

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