# Giai Bai Tap Tich Phan Suy Rong p2

• View
87

• Category

## Documents

Embed Size (px)

DESCRIPTION

tich phan suy rong dhbk le xuan dai

### Text of Giai Bai Tap Tich Phan Suy Rong p2

• GII BI TP TCH PHN SUY RNG

Bi ging in t

TS. L Xun i

Trng i hc Bch Khoa TP HCM

Khoa Khoa hc ng dng, b mn Ton ng dng

Email: ytkadai@hcmut.edu.vn

TP. HCM 2015.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 1 / 36

• Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1

Tnh tch phn suy rng loi 1

Cu 1

Tnh tch phn suy rng I =

+1

dx

xx2 + x + 1

.

t t =1

x x = 1

t dx = dt

t2.

i cn

x 1 +t 1 0

.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 2 / 36

• Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1

Tnh tch phn suy rng loi 1

Cu 1

Tnh tch phn suy rng I =

+1

dx

xx2 + x + 1

.

t t =1

x x = 1

t dx = dt

t2.

i cn

x 1 +t 1 0

.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 2 / 36

• Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1

Khi

I =

01

dtt2

1t .

1t2+ 1t + 1

=

10

dt1 + t + t2

=

10

d(t + 12

)(t + 12

)2+ 34

=

[ln

t + 12 +t2 + t + 1]1

0

= ln

(3

2+3

) ln

(3

2

)= ln

(1 +

23

).

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 3 / 36

• Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1

Tnh tch phn suy rng loi 1

Cu 2

Tnh tch phn suy rng I =

+1

arctan x

x2dx .

t

u = arctan xdv = dxx2

du =

dx

1 + x2

v = 1x

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 4 / 36

• Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1

Tnh tch phn suy rng loi 1

Cu 2

Tnh tch phn suy rng I =

+1

arctan x

x2dx .

t

u = arctan xdv = dxx2

du =

dx

1 + x2

v = 1x

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 4 / 36

• Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1

Khi

I =

[1x. arctan x

]+1

+

+1

dx

x(1 + x2)=

=pi

4+

+1

dx

x

+1

xdx

1 + x2=pi

4+

[ln |x | 1

2ln(1 + x2)

]+1

=

=pi

4+

[ln

x1 + x2]+

1

=pi

4+ ln 1 ln 1

2=pi

4+

ln 2

2

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 5 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

ngha hnh hc

Trong trng hp f (x) > 0,x [a,+), gi trca tch phn suy rng hi t c ngha hnh hc

l din tch ca hnh phng v hn c gi hn

bi x = a, trc Ox v th hm f (x)

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 6 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Ch .

T ngha hnh hc ca tch phn suy rng, ta

c nu tn ti gii hn hu hn v khc 0

limx+ f (x) = A 6= 0

v f (x) kh tch trn mi on [a, b] [a,+)th tch phn suy rng

+a

f (x)dx phn k

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 7 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

1

Nu > 1 th I =+a

dx

xhi t.

2

Nu 6 1 th I =+a

dx

xphn k.

1

Nu > 1 th I =+2

dx

x. ln xhi t.

2

Nu < 1 th I =+2

dx

x. ln xphn k.

3

Nu = 1 th I =+2

dx

x. ln xhi t nu

> 1, phn k nu 6 1.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

1

Nu > 1 th I =+a

dx

xhi t.

2

Nu 6 1 th I =+a

dx

xphn k.

1

Nu > 1 th I =+2

dx

x. ln xhi t.

2

Nu < 1 th I =+2

dx

x. ln xphn k.

3

Nu = 1 th I =+2

dx

x. ln xhi t nu

> 1, phn k nu 6 1.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

1

Nu > 1 th I =+a

dx

xhi t.

2

Nu 6 1 th I =+a

dx

xphn k.

1

Nu > 1 th I =+2

dx

x. ln xhi t.

2

Nu < 1 th I =+2

dx

x. ln xphn k.

3

Nu = 1 th I =+2

dx

x. ln xhi t nu

> 1, phn k nu 6 1.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

1

Nu > 1 th I =+a

dx

xhi t.

2

Nu 6 1 th I =+a

dx

xphn k.

1

Nu > 1 th I =+2

dx

x. ln xhi t.

2

Nu < 1 th I =+2

dx

x. ln xphn k.

3

Nu = 1 th I =+2

dx

x. ln xhi t nu

> 1, phn k nu 6 1.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

1

Nu > 1 th I =+a

dx

xhi t.

2

Nu 6 1 th I =+a

dx

xphn k.

1

Nu > 1 th I =+2

dx

x. ln xhi t.

2

Nu < 1 th I =+2

dx

x. ln xphn k.

3

Nu = 1 th I =+2

dx

x. ln xhi t nu

> 1, phn k nu 6 1.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Cu 3

Tm tch phn sau hi t I =

+1

dx

x 31 + x2

1

x 31 + x2

x+ 1x.x2/3

=1

x+2/3

tch phn I hi t th +2

3> 1 > 1

3.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 9 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Cu 3

Tm tch phn sau hi t I =

+1

dx

x 31 + x2

1

x 31 + x2

x+ 1x.x2/3

=1

x+2/3

tch phn I hi t th +2

3> 1 > 1

3.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 9 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Cu 4

Tm tch phn sau hi t

I =

+1

(2x + 3)dx

(4 + x) 31 + x4

Trng hp 1: > 0

(2x + 3)

(4 + x) 31 + x4

x+ 2xx.x4/3

=2

x+1/3

tch phn I hi t th +1

3> 1 > 2

3.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 10 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Cu 4

Tm tch phn sau hi t

I =

+1

(2x + 3)dx

(4 + x) 31 + x4

Trng hp 1: > 0

(2x + 3)

(4 + x) 31 + x4

x+ 2xx.x4/3

=2

x+1/3

tch phn I hi t th +1

3> 1 > 2

3.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 10 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Trng hp 2: = 0

(2x + 3)

(4 + x) 31 + x4

x+ 2x5.x4/3

=2

5x1/3

I phn k v1

3< 1

Trng hp 3: < 0

(2x + 3)

(4 + x) 31 + x4

x+ 2x4.x4/3

=1

2x1/3

I phn k v1

3< 1.

Vy tch phn I hi t th > 2/3.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 11 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Trng hp 2: = 0

(2x + 3)

(4 + x) 31 + x4

x+ 2x5.x4/3

=2

5x1/3

I phn k v1

3< 1

Trng hp 3: < 0

(2x + 3)

(4 + x) 31 + x4

x+ 2x4.x4/3

=1

2x1/3

I phn k v1

3< 1.

Vy tch phn I hi t th > 2/3.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 11 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Trng hp 2: = 0

(2x + 3)

(4 + x) 31 + x4

x+ 2x5.x4/3

=2

5x1/3

I phn k v1

3< 1

Trng hp 3: < 0

(2x + 3)

(4 + x) 31 + x4

x+ 2x4.x4/3

=1

2x1/3

I phn k v1

3< 1.

Vy tch phn I hi t th > 2/3.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 11 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Cu 5

Tm tch phn sau hi t

I =

+1

(3x + 4x)dx(5 + x)1

Trng hp 1: > 0

(3x + 4x)(5 + x)1

x+ 4xx(1)

=4

x(1)1

tch phn I hi t th

( 1) 1 > 1 > 2 < 1 > 2.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 12 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Cu 5

Tm tch phn sau hi t

I =

+1

(3x + 4x)dx(5 + x)1

Trng hp 1: > 0

(3x + 4x)(5 + x)1

x+ 4xx(1)

=4

x(1)1

tch phn I hi t th

( 1) 1 > 1 > 2 < 1 > 2.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 12 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Trng hp 2: = 0

(3x + 4x)(5 + x)1

x+ 4x61

=4

61.x1

I phn k v 1 < 1

Trng hp 3: < 0

(3x + 4x)(5 + x)1

x+ 4x51

=4

51.x1

I phn k v 1 < 1Vy tch phn I hi t th > 2.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 13 / 36

• Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t

Trng hp 2: = 0

(3x + 4x)(5 + x)1

x+ 4x61

=4

61.x1

I phn k v 1 < 1Trng hp 3: < 0

(3x + 4x)(5 + x)1

x+ 4x51

=4

51.x1

I phn k v 1 < 1

Vy tch phn I hi t th > 2.

TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY

Recommended

Documents
Documents
Documents
Documents
Documents
Documents
Design
Art & Photos
Education
Documents
Documents
Spiritual