Bbl6epwre epoe YTBP)KLIHH

I f(x)dx	=	f(x)dx - f f(x)dx
I f(x)dx	=	f(x)dx +	f(x)dx
I f(x)dx	=	f(x)dx +	f(x)dx

I f(x)dx = f f(x)dx - f f(x)dx

HellpepMBHOH Ha OT3K a; b], r,e a < b, YHKUHH f(x) HaM,LeTCH XOTH 6M oLHa TOqKa

t TaKa5l, ITO

f f(x)dx = f(t)(a - b)

f

f(t)

f(x)dx =

a b—a

f f(x)dx = f(t)(a + b)

f f(x)dx = f(t)(b - a)

f(x)dx MCHHO pae HOllH HrypbI, O6pa3OBaHHO KHBO y = f(x), HMMMH

x=a, x=b, y=O(a<b), eci

f(x) <0

f(x) 0

— f(x) — Bo3pacTaiowai 4YHKuH5I

f(x) 0

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y = 0, TO HI[OT1aLb 3T011 4HFypbI paa

If(x)dx

-If(x)dx

-If(x)dx

1(1- f(x))dx

ECJIH 4JHrypa o6pa3yeTc5l KHBbIMH y = f1 (x) H y = f2 (x) H H OT3K [a,b], re a = X1 H

b = x2 (x1 <x2) — a6cUHccM TOqeK LByX KpHBbIx, f1 (x) f2 (x), TO llh1OW)u

3T011 4JHFypbI HO 4opMyJ1e

b

S=S(f2(x)-f1(x))dx

a

b

S=S(f2(x)+f1(x))dx

S = S(f1(x)f2(x))dx

S = S(f1(x)-f2(x))dx

Ecrn f(x)dx =5, a f f(x)dx =3, TO f f(x)dx pae

Ecrn1f(x)dx =10, a ff(x)dx = 4, TO ff(x)dx pae

Ecrn f(x)dx =4, TO f (f(x) — 1)dx pae

Ecrn f(x)dx =5, TO f(1— f(x))dx pae

Ecrn If(x)dx =12, a Sf(x)dx =7, TO Sf(x)dx pae

HHTerpa I (k + f(x))dx pae

k+If(x)dx ff(x)dx b—a+klf(x)dx k(b-a)+ff(x)dx

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HHTerpa.r1, KOTOpMH He BMHCJ15ITC5I

KOHHbI HJTH 6ecKoHeHbI pee urn f(x)dx

a

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yr+1

HHTerpaI[ Ie3xdx pae

$ 7

dx

HHTerpaIl pae

1+x

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FluTerpaJI, OT KOTOOF1 He CYWCTBYT w1x1)epeHuHaY1

FlHTerpa.n OT Bo3pacTaIoeH cIYHKUHH

KOHHbI MJIM 6ecKoHeHbI upee urn f(x)dx

a—*—

a

+ (_ 4 -I X

HHTeFpaJI j 2 pae 2 4+x

1 dx

HHTeFpaJI $ pae o4_x2

2r

2r

$

x2dx

HuTerpall 3 pae

i 4+x

—11n5 3

—-GD

—in—

35

HHTerpaIl f eX xdx pae

Ecrn f(x)dx =7, TO (f(x) — 2)dx pae

$

tgxdx

HHTeFpaJI pae

,COS 2 X

HHTeFpaIL $ e2 xdx pae

$

2 xcix

HHTerpaIl pae

0 4 x2

2(1-k)

—1n4

—in— 24

2(-1)

2T

HHTerpa.n ctg2xdx pae

HHTerpaIl ftx+cos2x)dx pae

2r2 4

HHTerpaJI (2x — sin 2x)dx pae

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e 2

HHTeFpaJT f in xdx

Pae

.

HHTerpaJT [xcosxdx pae

2r+2

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Дата добавления: 2015-10-30