INTEGRAL 1 TRUE VALUE = .74682413281242 INTEGRAND = EXP(-X*X) INTERVAL = [0,1] N = 2 GAUSS = 7.4659468828286D-01 ERROR = 2.29D-04 N = 3 GAUSS = 7.4681458419126D-01 ERROR = 9.55D-06 N = 4 GAUSS = 7.4682446813099D-01 ERROR = -3.35D-07 N = 5 GAUSS = 7.4682412676625D-01 ERROR = 6.05D-09 N = 6 GAUSS = 7.4682413289016D-01 ERROR = -7.77D-11 N = 7 GAUSS = 7.4682413281164D-01 ERROR = 7.81D-13 N = 8 GAUSS = 7.4682413281243D-01 ERROR = -1.29D-14 N = 9 GAUSS = 7.4682413281243D-01 ERROR = -6.66D-15 N = 10 GAUSS = 7.4682413281243D-01 ERROR = -7.11D-15 N = 11 GAUSS = 7.4682413281243D-01 ERROR = -7.22D-15 N = 12 GAUSS = 7.4682413281243D-01 ERROR = -6.99D-15 N = 13 GAUSS = 7.4682413281243D-01 ERROR = -7.22D-15 N = 14 GAUSS = 7.4682413281243D-01 ERROR = -7.77D-15 N = 15 GAUSS = 7.4682413281243D-01 ERROR = -6.88D-15 N = 16 GAUSS = 7.4682413281243D-01 ERROR = -7.44D-15 N = 17 GAUSS = 7.4682413281243D-01 ERROR = -6.88D-15 N = 18 GAUSS = 7.4682413281243D-01 ERROR = -7.11D-15 N = 19 GAUSS = 7.4682413281243D-01 ERROR = -7.22D-15 N = 20 GAUSS = 7.4682413281243D-01 ERROR = -6.88D-15 INTEGRAL 2 TRUE VALUE = 1.3258176636680 INTEGRAND = 1/(1+X*X) INTERVAL = [0,4] N = 2 GAUSS = 1.3491124260355D+00 ERROR = -2.33D-02 N = 3 GAUSS = 1.3607171964140D+00 ERROR = -3.49D-02 N = 4 GAUSS = 1.3277132227954D+00 ERROR = -1.90D-03 N = 5 GAUSS = 1.3241128168242D+00 ERROR = 1.70D-03 N = 6 GAUSS = 1.3255440625029D+00 ERROR = 2.74D-04 N = 7 GAUSS = 1.3258821729886D+00 ERROR = -6.45D-05 N = 8 GAUSS = 1.3258388690841D+00 ERROR = -2.12D-05 N = 9 GAUSS = 1.3258163374843D+00 ERROR = 1.33D-06 N = 10 GAUSS = 1.3258163930568D+00 ERROR = 1.27D-06 N = 11 GAUSS = 1.3258176064321D+00 ERROR = 5.72D-08 N = 12 GAUSS = 1.3258177258893D+00 ERROR = -6.22D-08 N = 13 GAUSS = 1.3258176730164D+00 ERROR = -9.35D-09 N = 14 GAUSS = 1.3258176612862D+00 ERROR = 2.38D-09 N = 15 GAUSS = 1.3258176629276D+00 ERROR = 7.40D-10 N = 16 GAUSS = 1.3258176637204D+00 ERROR = -5.24D-11 N = 17 GAUSS = 1.3258176637129D+00 ERROR = -4.49D-11 N = 18 GAUSS = 1.3258176636698D+00 ERROR = -1.77D-12 N = 19 GAUSS = 1.3258176636658D+00 ERROR = 2.19D-12 N = 20 GAUSS = 1.3258176636677D+00 ERROR = 2.85D-13 INTEGRAL 3 TRUE VALUE = 3.6275987284680 INTEGRAND = 1/(2 + COS(X)) INTERVAL = [0,2*Pi] N = 2 GAUSS = 2.8042191325583D+00 ERROR = 8.23D-01 N = 3 GAUSS = 4.0574495155793D+00 ERROR = -4.30D-01 N = 4 GAUSS = 3.4509857122385D+00 ERROR = 1.77D-01 N = 5 GAUSS = 3.7088410789633D+00 ERROR = -8.12D-02 N = 6 GAUSS = 3.5921379211419D+00 ERROR = 3.55D-02 N = 7 GAUSS = 3.6434274581686D+00 ERROR = -1.58D-02 N = 8 GAUSS = 3.6206081800443D+00 ERROR = 6.99D-03 N = 9 GAUSS = 3.6306990941651D+00 ERROR = -3.10D-03 N = 10 GAUSS = 3.6262267518846D+00 ERROR = 1.37D-03 N = 11 GAUSS = 3.6282062971497D+00 ERROR = -6.08D-04 N = 12 GAUSS = 3.6273298112135D+00 ERROR = 2.69D-04 N = 13 GAUSS = 3.6277177636066D+00 ERROR = -1.19D-04 N = 14 GAUSS = 3.6275460462057D+00 ERROR = 5.27D-05 N = 15 GAUSS = 3.6276220437786D+00 ERROR = -2.33D-05 N = 16 GAUSS = 3.6275884106224D+00 ERROR = 1.03D-05 N = 17 GAUSS = 3.6276032943142D+00 ERROR = -4.57D-06 N = 18 GAUSS = 3.6275967080721D+00 ERROR = 2.02D-06 N = 19 GAUSS = 3.6275996224721D+00 ERROR = -8.94D-07 N = 20 GAUSS = 3.6275983328919D+00 ERROR = 3.96D-07 INTEGRAL 4 TRUE VALUE = -12.070346316390 INTEGRAND = EXP(X)*COS(X) INTERVAL = [0,Pi] N = 2 GAUSS = -1.2336210465695D+01 ERROR = 2.66D-01 N = 3 GAUSS = -1.2127420450175D+01 ERROR = 5.71D-02 N = 4 GAUSS = -1.2070189490295D+01 ERROR = -1.57D-04 N = 5 GAUSS = -1.2070328535889D+01 ERROR = -1.78D-05 N = 6 GAUSS = -1.2070346331102D+01 ERROR = 1.47D-08 N = 7 GAUSS = -1.2070346317532D+01 ERROR = 1.14D-09 N = 8 GAUSS = -1.2070346316389D+01 ERROR = -2.26D-13 N = 9 GAUSS = -1.2070346316390D+01 ERROR = 1.55D-13 N = 10 GAUSS = -1.2070346316390D+01 ERROR = 2.03D-13 N = 11 GAUSS = -1.2070346316390D+01 ERROR = 1.97D-13 N = 12 GAUSS = -1.2070346316390D+01 ERROR = 1.79D-13 N = 13 GAUSS = -1.2070346316390D+01 ERROR = 1.95D-13 N = 14 GAUSS = -1.2070346316390D+01 ERROR = 2.03D-13 N = 15 GAUSS = -1.2070346316390D+01 ERROR = 1.88D-13 N = 16 GAUSS = -1.2070346316390D+01 ERROR = 2.08D-13 N = 17 GAUSS = -1.2070346316390D+01 ERROR = 1.87D-13 N = 18 GAUSS = -1.2070346316390D+01 ERROR = 1.95D-13 N = 19 GAUSS = -1.2070346316390D+01 ERROR = 1.97D-13 N = 20 GAUSS = -1.2070346316390D+01 ERROR = 1.87D-13 INTEGRAL 5 TRUE VALUE = .66666666666667 INTEGRAND = SQRT(X) INTERVAL = [0,1] N = 2 GAUSS = 6.7388733867905D-01 ERROR = -7.22D-03 N = 3 GAUSS = 6.6917963389947D-01 ERROR = -2.51D-03 N = 4 GAUSS = 6.6782764537484D-01 ERROR = -1.16D-03 N = 5 GAUSS = 6.6729678969457D-01 ERROR = -6.30D-04 N = 6 GAUSS = 6.6704643791561D-01 ERROR = -3.80D-04 N = 7 GAUSS = 6.6691308508874D-01 ERROR = -2.46D-04 N = 8 GAUSS = 6.6683558010018D-01 ERROR = -1.69D-04 N = 9 GAUSS = 6.6678747456712D-01 ERROR = -1.21D-04 N = 10 GAUSS = 6.6675604293651D-01 ERROR = -8.94D-05 N = 11 GAUSS = 6.6673464017548D-01 ERROR = -6.80D-05 N = 12 GAUSS = 6.6671956337984D-01 ERROR = -5.29D-05 N = 13 GAUSS = 6.6670863693969D-01 ERROR = -4.20D-05 N = 14 GAUSS = 6.6670052508113D-01 ERROR = -3.39D-05 N = 15 GAUSS = 6.6669437659539D-01 ERROR = -2.77D-05 N = 16 GAUSS = 6.6668963149949D-01 ERROR = -2.30D-05 N = 17 GAUSS = 6.6668591108683D-01 ERROR = -1.92D-05 N = 18 GAUSS = 6.6668295298176D-01 ERROR = -1.63D-05 N = 19 GAUSS = 6.6668057148674D-01 ERROR = -1.39D-05 N = 20 GAUSS = 6.6667863265697D-01 ERROR = -1.20D-05 INTEGRAL 5 TRUE VALUE = .6666666666666667 INTEGRAND = SQRT(X) INTERVAL = [0,1] N APPROXIMATION ERROR RATIO DIFF 2 .67388733867904920 -7.221D-03 -6.739D-01 4 .66782764537484260 -1.161D-03 6.22 -6.060D-03 8 .66683558010017590 -1.689D-04 6.87 -9.921D-04 16 .66668963149948600 -2.296D-05 7.36 -1.459D-04 32 .66666966736785660 -3.001D-06 7.65 -1.996D-05 64 .66666705039818430 -3.837D-07 7.82 -2.617D-06 128 .66666671519048100 -4.852D-08 7.91 -3.352D-07 256 .66666667276753320 -6.101D-09 7.95 -4.242D-08