approximation integrals using three rules

IN MATLAB ONLY

Using these four functions, create a script to publish, writing a cell that uses N=10,20,40,80,160,320 to calculate the approximations to the integral below using each of the three rules. The script should calculate the values as well as the absolute errors for each rule and display them in a nicely formatted table, which should include the method, N, the approximate value, and the absolute error. To format the table, use

function:

function y=func(x)

y=sqrt(4−x^2);

end

The midpoint rule:

function y=Mid(a,b,N)

dx=(b-a)/N;

y=0;

for i=1:N

y=y+func(a+(i-0.5)*dx)*dx;

end

end

The trapezoidal rule:

function y=Trap(a,b,N)

dx=(b-a)/N;

y=0;

for i=1:N

y=y+0.5*(func(a+(i-1)*dx) + func(a+i*dx))*dx;

end

end

Simpson’s Rule:

function y=Simp(a,b,N)

dx=(b-a)/N;

y=0;

for i=1:N

y=y+(1/6)*(func(a+(i-1)*dx) + 4*func(a+(i-0.5)*dx) + func(a+i*dx))*dx;

end

end

fprintf('\%s | \%s | \%s | \%s \\n','N','Method','Value','AbsError')

[John D'Errico]

Are you just going to post all of the questions on your homework, with no reason shown?

Why are you asking this question? What is your problem?