Question

need help finishing this problem. matlab

erf(x) = 2-1 e_pdt Vr Joe Composte trapezoid rule (MATLAB trapz andlor cuntrapr tunctions) Three point Gauss-Legendre quadrature MATLAB's builb-in integral function (Adaptive Gauss-Kronrod Quadrature) Write a function that receives the following single input 1. A column vector of one or more values at which el) is to be computed Your function should reburn the following outputs (in order, column vectors when input is a vector) 1. The estimate(s) for ert) caculated using composite trapezoid rule between 0 and each of the elements in x Evaluate the integrand at 0 and at the input s-values to compute y vaues for the traperoid r 2. The estimate(s) of er) caloulated using three point Gauss-Legendre quadrature Work by hand to develop the shted integrand (in serms of ) and use the appropriate constants and function evaluata The estimate(s) of erf) caculated using MATLABs buit-in integral function Your Function 11 function erfIntegral] = PA7_crfIntegration(x) [erfTrapezoid, erfGL3, 2 | 3 A = 2. /sqrt(pi) % constant value outside of integral 4) Fox @(t) expC-(t)^2); % f(x) that is being integrated 5 integrat ionLimits(1) = θ = x(i); integrat ionLinits(1+1)

Answer 1

`Hey,

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function [erfTrapezoid,erfGL3,erfIntegral]=PA7_erfIntegration(x)
erfTrapezoid=[];
erfGL3=[];
erfIntegral=[];
f=@(x) (2/sqrt(pi))*exp(-x.^2);
c = [0.5555556 0.8888889 0.5555556]; % weight coefficients

xxx = [-0.774596669 0 0.774596669];

for i=1:length(x)
xx=linspace(0,x(i));
  
erfTrapezoid(i)=trapz(xx,f(xx));
erfIntegral(i)=integral(f,0,x(i));
yyy = (x(i))/2 + (x(i))/2 * xxx;

erfGL3(i) = (x(i))/2 * sum(c.*f(yyy));
end
erfTrapezoid=erfTrapezoid';
erfIntegral=erfIntegral';
erfGL3=erfGL3';
end

Kindly revert for any queries

Thanks.