Using multiple integration methods in one script

Hi, I have to calculate an integral using the midpoint, trapezoid, and simpson's methods. I already have the functions stored in one file in Matlab, but I am encountering difficulty when trying to use them all in one script. I have the integral (sqrt(4-x^2)) saved in a function (called Func). These three methods each call Func. I would appreciate any hints or tips that anyone can give me. THIS IS A SCHOOL ASSIGNMENT, SO NO COMPLETE ANSWERS. Here is my script (eventually, N will contain an array of numbers):

%Approximating an Integral using multiple methods

y=0;

sum=0;

a=0;

b=2;

for N=[10]

Mid(a,b,N)

midval=sum

abserror=pi-y

Trap(a,b,N)

trapval=sum

abserror=pi-y

Simp(a,b,N)

simpval=sum

abserror=pi-y

end

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

Answer 1

[David Hill]

Func=@(x)sqrt(4-x^2);
Integral=@(x)2*asin(x/2)+x*sqrt(4-x^2)/2;
a=0;
b=2;
N=10;
m=Mid(a,b,N,Func);
t=Trap(a,b,N,Func);
s=Simp(a,b,N,Func);

I would pass Func to your integration functions. You will get answers back (m,t,s) from each of your functions that you can compare to the actual evaluation of the actual integral.