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function R(f,a,b,n){var r=0,d=(b-a)/n;for(var i=0;i<n;i++){r+=f(a+i*d);}return r*d;}function T(f,a,b,n){var d=(b-a)/n,r=f(a)+f(b);for(var i=1;i<n;i++){r+=2*f(a+i*d);}return r*d/2;}function S(f,a,b,n){if(n%2!==0)n++;var h=(b-a)/n,s=f(a)+f(b);for(var i=1;i<n;i++){s+=(i%2==0?2:4)*f(a+i*h);}return s*h/3;}function M(f,a,b){var c=(a+b)/2;return(b-a)*f(c);}function E(f,a,b,n,ex){return Math.abs(S(f,a,b,n)-ex);}var f=function(x){return Math.sin(x)*Math.exp(-x*x)};var ex=S(f,0,3.14159,10000);console.log("Riemann="+R(f,0,3.14159,1000));console.log("Trapezoidal="+T(f,0,3.14159,1000));console.log("Simpson="+S(f,0,3.14159,1000));console.log("Midpoint="+M(f,0,3.14159));console.log("Error="+E(f,0,3.14159,1000,ex));function avgError(f,a,b,n){var re=R(f,a,b,n),te=T(f,a,b,n),se=S(f,a,b,n);return(Math.abs(se-re)+Math.abs(se-te))/2;}function steps(n){var arr=[];for(var i=1;i<=n;i*=2){arr.push(i);}return arr;}function analyze(f,a,b){var result={};steps(64).forEach(function(n){result[n]={riemann:R(f,a,b,n),trapezoid:T(f,a,b,n),simpson:S(f,a,b,n),error:E(f,a,b,n,ex)};});return result;}var report=analyze(f,0,3.14159);for(var k in report){console.log("n="+k+" R="+report[k].riemann.toFixed(6)+" T="+report[k].trapezoid.toFixed(6)+" S="+report[k].simpson.toFixed(6)+" Error="+report[k].error.toExponential(2));}