12(1/x) dx, approximately 0.6931471806
n=Left Hand RuleTrapezoid RuleSimpson's Rule
10  
100  
1,000  
10,000  
100,000  		 0.7187714032
0.6956534302
0.6933972431
0.6931721811
0.6931496806		 0.6937714035
0.6931534305
0.6931472430
0.6931471810
 		 0.6931473748
0.6931471808
0.6931471803
 
 
01(4/{1+x2) dx, approximately 3.141592654 (Pi)
n=Left Hand RuleTrapezoid RuleSimpson's Rule
10  
100  
1,000  
10,000  
100,000  		 3.239925989
3.151575986
3.142592487
3.141692652
3.141602654		 3.139925989
3.141575988
3.142592487
3.141592652
 		 3.141592652
3.141592653