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(2- )

. f(x) - [0,2]

. P t-1<1<t . i mi=Mi=0 . (m, M .) m=0, M=1 .

. U(f,P) - L(f,P) = t - t-1 . , , . v >0 -

U(f,P) - L(f,P) <

. t - t-1 < .

.

vv . v v . v ( ) - v v . v v vv vvv.

f(x)=x2 . [0, b] f - . P - (ti-ti-1) v v b/n . t0=0, t1=b/n, t2=2b/n,..., ti=ib/n .

. 12+...+k2=(1/6)k(k+1)(2k+1)

. L(f,P) b3/3 U(f,P) ,

. v ? v :

, b=3 v . 27/3=9 !

. v ( - ). v v. ( . , .)

21

a < c < b . f [a, b] f [a, c] , [c, b]

.

22

f, g [a, b] f+g [a, b]

.

23

f, g [a, b] fg [a, b] .

24

f [a, b] cf [a, b]

.

25

f [a, b] [a, b] v - m f(x) M

.

P m(b-a) L(f,P), U(f,P) M(b-a) .

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f [a, b] F - [a, b]

F [a, b] v .

v ... .

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