test gauleg.m on interval -1.0 to 1.0 ordinates, weights x1(1)= 0.0000000000000E+000, w1(0)= 2.0000000000000E+000 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-5.7735026918963E-001, w1(0)= 1.0000000000000E+000 x1(2)= 5.7735026918963E-001, w1(0)= 1.0000000000000E+000 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-7.7459666924148E-001, w1(0)= 5.5555555555556E-001 x1(2)= 0.0000000000000E+000, w1(0)= 8.8888888888889E-001 x1(3)= 7.7459666924148E-001, w1(0)= 5.5555555555556E-001 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-8.6113631159405E-001, w1(0)= 3.4785484513745E-001 x1(2)=-3.3998104358486E-001, w1(0)= 6.5214515486255E-001 x1(3)= 3.3998104358486E-001, w1(0)= 6.5214515486255E-001 x1(4)= 8.6113631159405E-001, w1(0)= 3.4785484513745E-001 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.0617984593866E-001, w1(0)= 2.3692688505619E-001 x1(2)=-5.3846931010568E-001, w1(0)= 4.7862867049937E-001 x1(3)= 0.0000000000000E+000, w1(0)= 5.6888888888889E-001 x1(4)= 5.3846931010568E-001, w1(0)= 4.7862867049937E-001 x1(5)= 9.0617984593866E-001, w1(0)= 2.3692688505619E-001 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.3246951420315E-001, w1(0)= 1.7132449237917E-001 x1(2)=-6.6120938646626E-001, w1(0)= 3.6076157304814E-001 x1(3)=-2.3861918608320E-001, w1(0)= 4.6791393457269E-001 x1(4)= 2.3861918608320E-001, w1(0)= 4.6791393457269E-001 x1(5)= 6.6120938646626E-001, w1(0)= 3.6076157304814E-001 x1(6)= 9.3246951420315E-001, w1(0)= 1.7132449237917E-001 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.4910791234276E-001, w1(0)= 1.2948496616887E-001 x1(2)=-7.4153118559939E-001, w1(0)= 2.7970539148928E-001 x1(3)=-4.0584515137740E-001, w1(0)= 3.8183005050512E-001 x1(4)= 0.0000000000000E+000, w1(0)= 4.1795918367347E-001 x1(5)= 4.0584515137740E-001, w1(0)= 3.8183005050512E-001 x1(6)= 7.4153118559939E-001, w1(0)= 2.7970539148928E-001 x1(7)= 9.4910791234276E-001, w1(0)= 1.2948496616887E-001 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.6028985649754E-001, w1(0)= 1.0122853629038E-001 x1(2)=-7.9666647741363E-001, w1(0)= 2.2238103445337E-001 x1(3)=-5.2553240991633E-001, w1(0)= 3.1370664587789E-001 x1(4)=-1.8343464249565E-001, w1(0)= 3.6268378337836E-001 x1(5)= 1.8343464249565E-001, w1(0)= 3.6268378337836E-001 x1(6)= 5.2553240991633E-001, w1(0)= 3.1370664587789E-001 x1(7)= 7.9666647741363E-001, w1(0)= 2.2238103445337E-001 x1(8)= 9.6028985649754E-001, w1(0)= 1.0122853629038E-001 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.6816023950763E-001, w1(0)= 8.1274388361575E-002 x1(2)=-8.3603110732664E-001, w1(0)= 1.8064816069486E-001 x1(3)=-6.1337143270059E-001, w1(0)= 2.6061069640294E-001 x1(4)=-3.2425342340381E-001, w1(0)= 3.1234707704000E-001 x1(5)= 0.0000000000000E+000, w1(0)= 3.3023935500126E-001 x1(6)= 3.2425342340381E-001, w1(0)= 3.1234707704000E-001 x1(7)= 6.1337143270059E-001, w1(0)= 2.6061069640294E-001 x1(8)= 8.3603110732664E-001, w1(0)= 1.8064816069486E-001 x1(9)= 9.6816023950763E-001, w1(0)= 8.1274388361575E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.7390652851717E-001, w1(0)= 6.6671344308688E-002 x1(2)=-8.6506336668898E-001, w1(0)= 1.4945134915058E-001 x1(3)=-6.7940956829902E-001, w1(0)= 2.1908636251598E-001 x1(4)=-4.3339539412925E-001, w1(0)= 2.6926671931000E-001 x1(5)=-1.4887433898163E-001, w1(0)= 2.9552422471475E-001 x1(6)= 1.4887433898163E-001, w1(0)= 2.9552422471475E-001 x1(7)= 4.3339539412925E-001, w1(0)= 2.6926671931000E-001 x1(8)= 6.7940956829902E-001, w1(0)= 2.1908636251598E-001 x1(9)= 8.6506336668898E-001, w1(0)= 1.4945134915058E-001 x1(10)= 9.7390652851717E-001, w1(0)= 6.6671344308688E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.7822865814606E-001, w1(0)= 5.5668567116174E-002 x1(2)=-8.8706259976810E-001, w1(0)= 1.2558036946490E-001 x1(3)=-7.3015200557405E-001, w1(0)= 1.8629021092773E-001 x1(4)=-5.1909612920681E-001, w1(0)= 2.3319376459199E-001 x1(5)=-2.6954315595234E-001, w1(0)= 2.6280454451025E-001 x1(6)= 0.0000000000000E+000, w1(0)= 2.7292508677790E-001 x1(7)= 2.6954315595234E-001, w1(0)= 2.6280454451025E-001 x1(8)= 5.1909612920681E-001, w1(0)= 2.3319376459199E-001 x1(9)= 7.3015200557405E-001, w1(0)= 1.8629021092773E-001 x1(10)= 8.8706259976810E-001, w1(0)= 1.2558036946490E-001 x1(11)= 9.7822865814606E-001, w1(0)= 5.5668567116174E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.8156063424672E-001, w1(0)= 4.7175336386512E-002 x1(2)=-9.0411725637047E-001, w1(0)= 1.0693932599532E-001 x1(3)=-7.6990267419430E-001, w1(0)= 1.6007832854335E-001 x1(4)=-5.8731795428662E-001, w1(0)= 2.0316742672307E-001 x1(5)=-3.6783149899818E-001, w1(0)= 2.3349253653835E-001 x1(6)=-1.2523340851147E-001, w1(0)= 2.4914704581340E-001 x1(7)= 1.2523340851147E-001, w1(0)= 2.4914704581340E-001 x1(8)= 3.6783149899818E-001, w1(0)= 2.3349253653835E-001 x1(9)= 5.8731795428662E-001, w1(0)= 2.0316742672307E-001 x1(10)= 7.6990267419430E-001, w1(0)= 1.6007832854335E-001 x1(11)= 9.0411725637047E-001, w1(0)= 1.0693932599532E-001 x1(12)= 9.8156063424672E-001, w1(0)= 4.7175336386512E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.8418305471859E-001, w1(0)= 4.0484004765316E-002 x1(2)=-9.1759839922298E-001, w1(0)= 9.2121499837728E-002 x1(3)=-8.0157809073331E-001, w1(0)= 1.3887351021979E-001 x1(4)=-6.4234933944034E-001, w1(0)= 1.7814598076195E-001 x1(5)=-4.4849275103645E-001, w1(0)= 2.0781604753689E-001 x1(6)=-2.3045831595513E-001, w1(0)= 2.2628318026290E-001 x1(7)= 1.2325951644078E-032, w1(0)= 2.3255155323087E-001 x1(8)= 2.3045831595513E-001, w1(0)= 2.2628318026290E-001 x1(9)= 4.4849275103645E-001, w1(0)= 2.0781604753689E-001 x1(10)= 6.4234933944034E-001, w1(0)= 1.7814598076195E-001 x1(11)= 8.0157809073331E-001, w1(0)= 1.3887351021979E-001 x1(12)= 9.1759839922298E-001, w1(0)= 9.2121499837728E-002 x1(13)= 9.8418305471859E-001, w1(0)= 4.0484004765316E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.8628380869681E-001, w1(0)= 3.5119460331752E-002 x1(2)=-9.2843488366357E-001, w1(0)= 8.0158087159760E-002 x1(3)=-8.2720131506977E-001, w1(0)= 1.2151857068790E-001 x1(4)=-6.8729290481169E-001, w1(0)= 1.5720316715819E-001 x1(5)=-5.1524863635815E-001, w1(0)= 1.8553839747794E-001 x1(6)=-3.1911236892789E-001, w1(0)= 2.0519846372130E-001 x1(7)=-1.0805494870734E-001, w1(0)= 2.1526385346316E-001 x1(8)= 1.0805494870734E-001, w1(0)= 2.1526385346316E-001 x1(9)= 3.1911236892789E-001, w1(0)= 2.0519846372130E-001 x1(10)= 5.1524863635815E-001, w1(0)= 1.8553839747794E-001 x1(11)= 6.8729290481169E-001, w1(0)= 1.5720316715819E-001 x1(12)= 8.2720131506977E-001, w1(0)= 1.2151857068790E-001 x1(13)= 9.2843488366357E-001, w1(0)= 8.0158087159760E-002 x1(14)= 9.8628380869681E-001, w1(0)= 3.5119460331752E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 x1(1)=-9.8799251802049E-001, w1(0)= 3.0753241996117E-002 x1(2)=-9.3727339240071E-001, w1(0)= 7.0366047488108E-002 x1(3)=-8.4820658341043E-001, w1(0)= 1.0715922046717E-001 x1(4)=-7.2441773136017E-001, w1(0)= 1.3957067792615E-001 x1(5)=-5.7097217260854E-001, w1(0)= 1.6626920581699E-001 x1(6)=-3.9415134707756E-001, w1(0)= 1.8616100001556E-001 x1(7)=-2.0119409399743E-001, w1(0)= 1.9843148532711E-001 x1(8)= 1.2325951644078E-032, w1(0)= 2.0257824192556E-001 x1(9)= 2.0119409399743E-001, w1(0)= 1.9843148532711E-001 x1(10)= 3.9415134707756E-001, w1(0)= 1.8616100001556E-001 x1(11)= 5.7097217260854E-001, w1(0)= 1.6626920581699E-001 x1(12)= 7.2441773136017E-001, w1(0)= 1.3957067792615E-001 x1(13)= 8.4820658341043E-001, w1(0)= 1.0715922046717E-001 x1(14)= 9.3727339240071E-001, w1(0)= 7.0366047488108E-002 x1(15)= 9.8799251802049E-001, w1(0)= 3.0753241996117E-002 integral(1.0, -1.0..1.0)= 2.0000000000000E+000 integral (0.5,1.0) sin(x) dx = 3.3727533740282E-001 integral (0.5,1.0) sin(x) dx = 3.3728025865871E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602149E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602223E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602223E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602223E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602223E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602223E-001 integral (0.5,1.0) sin(x) dx = 3.3728025602223E-001 -cos(1.0)+cos(0.5) = 3.3728025602223E-001 Maple says 3.372802560E-001