4 kısmi i̇ntegral

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Kısmi İntegral

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Page 1: 4 kısmi i̇ntegral

Kısmi İntegral

Page 2: 4 kısmi i̇ntegral

Formül :

duvvuudvdxxfxf ..)(').(

LAPTÜ Kuralı

Page 3: 4 kısmi i̇ntegral

ÖRNEK SORULAR

?.)1 3 dxex x

dudx

ux

vIne

e

dvdxe

x

x

.3

3

3

duvvuudvdxxfxf ..)(').(

duvvudxex x ... 3

dxee

xxx

33.

33

cee

xxx

3.

3

1

3.

33

Page 4: 4 kısmi i̇ntegral

?)2 5Inxdxx

dxx

du

Inxu

1

vx

dvdxx

6

6

5

duvvuudvdxxfxf ..)(').(

dxx

xxInxInxdxx

1.

66

. 665

cxxInx

6.

6

1

6

. 66

Page 5: 4 kısmi i̇ntegral

?arctan)3 xdx

duvvuxdx ..arctandx

xdu

xu

21

1

arctan

xv

dxdv

2

2

1 2

dtxdx

dtxdx

tx

dxx

xxx21

1.).(arctan

t

dtxx

2).(arctan

cIntxx2

1.arctan

cxInxx )1(2

1.arctan 2

Page 6: 4 kısmi i̇ntegral

?)1(

.)4

2dx

x

ex x

dudxex

dudxexe

uex

x

xx

x

)1(

).(

.

vx

t

t

dt

dtdx

tx

dvx

dx

1

1

1

1

)1(

1

2

2

duvuv .

dxexxx

ex xx

)1(1

1

1

)1(.

cex

xe xx

1

.

Page 7: 4 kısmi i̇ntegral

?2sin.)5 xdxx

duvuv .dxdu

xu

vx

dvxdx

2

2cos

2sin

dxxx

x2

2cos)

2

2cos.(

cxxx

2sin4

1

2

).2(cos

Page 8: 4 kısmi i̇ntegral

?sin)6 xdxeI x

duxdx

ux

cos

sin

ve

dvdxe

x

x

duxdx

ux

sin

cos

duvuv .

xdxeexI xx cos.).(sin

xdxeexxdxeII xxx sin.coscos.)

IxeexI xx cos)(sin

IxexeI xx cossin

2

cossin xx xexeI