, %#/ 23 2. # #' # & # * # $ %## #
. # # / + + # # + * + (3) # (5), #" (# * +#
S (P, X; f ) < f1 (x)dx + 2M (m -1)l < I ( f ) + (1+ 2M )e + e = I ( f ) + 2(1 + M )e.
—
# #) ! # ** 2( #/ # ( 2, ) * 6 * + d>0 , ) ( / +* " l, 0 < l < d¢¢, +! / */ * +#
S(P, X; f) > I(f) - 2(1 + M)e.
. 2#+ d = min{d¢, d¢¢} # 0 #+ `I(f) = I(f) # & # $ %## f, 0 #7 (+ * ( #" * +#/ + * ( 6 +#(
"e > 0$d > 0"P"X0 < l < d S (P, X; f ) - f (x)dx < 2(1+ M )e,
—
) + *# * +#
lim S (P, X; f ) = f (x)dx
l®0
—
# ( 0!+ 3" (# * + 2( #/ ! 1.
. '( ( 0 * + ( * ) * # + 2( #/ ! 1. .*
"e > 0 $d > 0 "P "X 0 < l < d |S(P, X; f) - I| < e.
. 2, ) $ %#/ f # & # 0 [a, b].
!3 #0+ 03# # P = {x0, x1, x2, ..., xn-1, xn} 0 [a, b] * (# l < d # 2# D1 = [x0, x1], D2 = (x1, x2], ..., Dn = (xn-1, xn]. &( ( / 3 & 3 ) X = {x1, x2, ..., xn} +! / */ + * +
n
f (xk ) Dk - I < e.
k =1
. *
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