Area under the graph  y = x*x  from  x=0  to  x=1 

     n = 1          0.00000  <  AREA  <  1.00000 
     n = 2          0.12500  <  AREA  <  0.62500 
     n = 4          0.21875  <  AREA  <  0.46875 
     n = 8          0.27344  <  AREA  <  0.39844 
     n = 16         0.30273  <  AREA  <  0.36523 
     n = 32         0.31787  <  AREA  <  0.34912 
     n = 64         0.32556  <  AREA  <  0.34119 
     n = 128        0.32944  <  AREA  <  0.33725 
     n = 256        0.33138  <  AREA  <  0.33529 
     n = 512        0.33236  <  AREA  <  0.33431 
     n = 1024       0.33284  <  AREA  <  0.33382 
     n = 2048       0.33309  <  AREA  <  0.33358 
     n = 4096       0.33321  <  AREA  <  0.33346 
     n = 8192       0.33327  <  AREA  <  0.33339 
     n = 16384      0.33330  <  AREA  <  0.33336 
     n = 32768      0.33332  <  AREA  <  0.33335 
     n = 65536      0.33333  <  AREA  <  0.33334