数值积分——复合梯形求积公式

%%复合梯形求积公式
%%Y是数值（attribute=0）或具体表达式（attribute=1），interval是求积区间，n是精度（如果是数值，则为数值长度-1）
function CTQF = Compound_trapezoid_quadrature_formula(Y,interval,n,attribute)
a = interval(1);b = interval(2);
h = (b-a)/n;
if attribute == 0
    sum = 0;
    for i=1:1:n-1
        sum=sum+Y(i+1);
    end
    Tn = (Y(1)+Y(n+1)+2*sum)*h/2;
    CTQF = vpa(Tn,8);
elseif attribute == 1
    syms x;
    X(1) = a;
    X(n+1) = b;
    for i=1:1:n-1
        X(i+1)=a+i*h;
    end
    sum=0;
    for i=1:1:n-1
        sum=sum+subs(Y,x,X(i+1));
    end
    Tn=(subs(Y,x,a)+subs(Y,x,b)+2*sum)*h/2;
    CTQF = vpa(Tn,8);
end

syms x;
Y = exp(x)*sin(x)+log(x+1);
interval=[0 pi];
attribute = 1;
n = 1000;
Compound_trapezoid_quadrature_formula(Y,interval,n,attribute)

vpa(int(Y,x,interval),8)

ans =
14.814269
ans =
14.81429