${\xi }_i$

$S_n$

$n=100$

$n=1000$

$n=10000$

左端点

${\displaystyle \sum _{i=0}^{n-1}{\text{e}}^{x_i}{n}^{-1}}$

1.633799

1.709705

1.717423

1.718196

右端点

${\displaystyle \sum _{i=1}^n{\text{e}}^{x_i}{n}^{-1}}$

1.805628

1.726888

1.719141

1.718368

中点

1.717566

1.718275

1.718282

1.718282