Integral 1: f(x)=cos(x) on [0.0,pi/2] Intervals Trapez. Simpson 2 0.948059 1.002280 4 0.987116 1.000135 8 0.996785 1.000008 16 0.999197 1.000001 32 0.999799 1.000000 64 0.999950 1.000000 128 0.999987 1.000000 256 0.999997 1.000000 512 0.999999 1.000000 1024 1.000000 1.000000 2048 1.000000 1.000000 4096 1.000000 1.000000 8192 1.000000 1.000000 16384 1.000000 1.000000 32768 1.000000 1.000000 65536 1.000000 1.000000 131072 1.000000 1.000000 262144 1.000000 1.000000 quanc8 = 1.000000 gauss8 = 1.000000 Integral 2: f(x)=4/(x^2+1) on [0.0,1.0] Intervals Trapez. Simpson 2 3.100000 3.133333 4 3.131176 3.141569 8 3.138988 3.141593 16 3.140942 3.141593 32 3.141430 3.141593 64 3.141552 3.141593 128 3.141582 3.141593 256 3.141590 3.141593 512 3.141592 3.141593 1024 3.141592 3.141593 2048 3.141593 3.141593 4096 3.141593 3.141593 8192 3.141593 3.141593 16384 3.141593 3.141593 32768 3.141593 3.141593 65536 3.141593 3.141593 131072 3.141593 3.141593 262144 3.141593 3.141593 quanc8 = 3.141593 gauss8 = 3.141593 Integral 3: f(x)=(x-1)^(1/5)/(x^2+1) on [1.0,5.0] Intervals Trapez. Simpson 2 0.280490 0.340153 4 0.413523 0.457868 8 0.491038 0.516876 16 0.529498 0.542318 32 0.547242 0.553157 64 0.555179 0.557825 128 0.558679 0.559846 256 0.560212 0.560723 512 0.560882 0.561105 1024 0.561174 0.561271 2048 0.561301 0.561343 4096 0.561356 0.561375 8192 0.561380 0.561388 16384 0.561391 0.561394 32768 0.561395 0.561397 65536 0.561397 0.561398 131072 0.561398 0.561399 262144 0.561399 0.561399 quanc8 = 0.561399 gauss8 = 0.562762 Integral 4: f(x)= 1 - cos(32.0*x) on [0.0,2*pi] Intervals Trapez. Simpson 2 0.000000 0.000000 4 0.000000 0.000000 8 0.000000 0.000000 16 0.000000 0.000000 32 0.000000 0.000000 64 6.283185 8.377580 128 6.283185 6.283185 256 6.283185 6.283185 512 6.283185 6.283185 1024 6.283185 6.283185 2048 6.283185 6.283185 4096 6.283185 6.283185 8192 6.283185 6.283185 16384 6.283185 6.283185 32768 6.283185 6.283185 65536 6.283185 6.283185 131072 6.283185 6.283185 262144 6.283185 6.283185 quanc8 = 3.141593 gauss8 = 6.295211 Integral 5: f(x,y)= (x+y)^2 on [0.0,1.0; 0.0,1.0] integral = 1.166667 Integral 6: f(x,y)= x^2/(y^2+1) on [0.0,1.0; 0.0,sin(x)] integral = 0.194330 Error Function x Tables Integral 0.0 0.000000 0.000000 0.2 0.222703 0.222703 0.4 0.428392 0.428392 0.6 0.603856 0.603856 0.8 0.742101 0.742101 1.0 0.842701 0.842701 1.2 0.910314 0.910314 1.4 0.952285 0.952285 1.6 0.976348 0.976348 1.8 0.989091 0.989091 2.0 0.995322 0.995322