, %#/ 21 3. + '* + + " & # #2 & # & +
[a, b],
m(b - a) £ I(f) £ M(b - a).
. %#/ f $# # # & #) + * * $ %# ' (-f), / ( + + / + * + -M £ -f(x) £ -m + ) " 0 [a, b]. . 1 * 6 * + + " #' # & `I(-f) # -M(b - a) £ `I(-f) £ -m(b - a). .(* + // + 1 # + * + `I(-f) = -I(f) # 2 / #" (-1), #" (# + 2( # * (* +#/ # 0 )#+ & ( 0 * +.
& & + /, * 7 # `I(-f) = -I(f) * + ( #+ + ( 2 ## * 6 * + + #/ 2( & #0 #* !" # & +.
. 1 + ( 0 * + (* +#/ 2 3! +! 7 & ( 0 * 6 * + + # #2 & # & I(f) * (* + #, ) ! # ( 0 * + ! 1.
3.
. 2, ) + " #' # & #7 ) * #) 3 ( *+ '* + # # ' * #.
2. ! % # f g % a ³ 0. " (
`I(af) = a`I(f),
`I(f + g) £ `I(f) + `I(g).
. * # $ %## f # g $# # ! # & #) !, # # 2 /+ / */ # $ %## af # f + g.
* # a = 0, $ %#/ af = 0 # + ' # & # $ + 2 ) +#( .
. * a > 0. &(
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f |
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I (af ) = inf |
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(x)dx = inf |
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dx = |
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f ³af |
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f |
³ f |
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— |
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a |
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— |
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212