江画工太猩院 211321mn+1)(2n+4 1n)nn百n 几→>0→n x dx =lim ∑△x i=1 lim1+-2+ n→0 3江西理工大学理学院 n n i n i 1 2 1 ⎟ ⋅ ⎠ ⎞ ⎜ ⎝ ⎛ = ∑= ∑= = n i i n 1 2 3 1 6 1 ( 1)( 2 1 ) 3 + + = ⋅ n n n n , 1 2 1 1 6 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛ = + n n λ → 0 ⇒ n → ∞ x dx ∫ 1 0 2 i i n i = ∑ ∆x = → 2 1 0 lim ξ λ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛ = + n → ∞ n n 1 2 1 1 6 1 lim . 3 1 =