Requirements:
1. Write a numerical integration function. The input is the upper and lower limits of integration, the number of segments, the integrand, and the integration method; the
method of compound integration is required. The function includes three compound integration methods: T, Simpson, and Cotes.
matlab code:
① main function
function y=integral(a,b,n,fun,flag)
%a,b积分上下限，n分段段数，fun被积函数，flag积分方法： 1:T,2:S,3:C
h=(b-a)/n;
s0=0;
fa=subs(fun,a);
fb=subs(fun,b);
if flag==1
for k = 1:n-1
xk = a+k*h;
s0 = s0+subs(fun,xk);
end
y = (h/2)*(fa+2*s0+fb);
end
if flag==2
s1=subs(fun,a+0.5*h);
for k = 1:n-1
xk = a+k*h;
s0 = subs(fun,xk)+s0;
s1 = subs(fun,xk+(h/2))+s1;
end
y=(h/6)*(fa+2*s0+4*s1+fb);
end
if flag==3
s1=0;
s2=0;
s3=0;
for k = 1:n-1
xk = a+k*h;
s0 = s0+subs(fun,xk);
end
for k = 0:n-1
xk = a+k*h;
s1 = subs(fun,xk+(h/4))+s1;
s2 = subs(fun,xk+(h/2))+s2;
s3 = subs(fun,xk+(3*h/4))+s3;
end
y=(h/90)*(7*fa+32*s1+12*s2+32*s3+14*s0+7*fb);
end