jawaban tugas 1 kalkulus 2

3

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Buat peserta kuliah Kalkulus 2 TI.Unpar 2009/2010Jawaban tugas pertama, tugas 2nya menyusul

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Page 1: Jawaban Tugas 1 Kalkulus 2

1. ∫ ∫ +−−+=

−+−+ dx

xxxxdx

xxxx

)12)(1(12

24312

223

221)22)(1(12

22 +−++

−=

+−−+

xxCBx

xA

xxxx

)22)(1()1)(()22(

2

2

+−−−+++−=

xxxxCBxxxA

53

312

220

)1)(()22(12 2

=−=

==−

=+−−=+

−+++−=+

CBA

CACBA

BAxCBxxxAx

∫∫∫ +−+−+

−=

+−−+ dx

xxxdx

xdx

xxxx

2253

13

)12)(1(12

22

Cxxxx

xdxxxx

dxxx

xxx

dxxx

xx

+−++−+−=

+−++−+−=

+−++−+−=

+−

+−−+−=

|1|arctan8|22|ln23|1|ln3

1)1(8|22|ln

23|1|ln3

228|22|ln

23|1|ln3

22

8)22(23

|1|ln3

2

22

22

2

2. ∫ −−+ dxxxx

2)2)(1(23

22 )2(21)2)(1(23

−+

−+

−=

−−+

xC

xB

xA

xxx

2

2

)2)(1()1()2)(1()2(

−−−+−−+−=

xxxCxxBxA

85

5224

3340

)1()23()44(23 22

=−=

==−+

=+−−=+

−++−++−=+

CBA

CBACBA

BAxCxxBxxAx

Page 2: Jawaban Tugas 1 Kalkulus 2

∫∫∫∫ −+

−−+

−=

−−+ dx

xdx

xdx

xdx

xxx

22 )2(8

25

15

)2)(1(23

Cxx

x +−

−−−=

28

21ln5

3. ∫ −−dx

eee

xx

x

22

tdt

tttdx

eee

tdtdxdxedtet

subtitusi

xx

x

xx

⋅−=

=−−

=⇒=→=

∫∫ 22 22

∫ −−=

22 ttdt

)1)(2(1

21

2 +−=

−− tttt

)1)(2()2()1(

12

+−−++=

++

−=

tttBtA

tB

tA

∫∫ +

−+

−=

−−

−=→−=

=→=

13

1

23

1

2

311

312

2 t

dt

t

dt

ttdt

Bt

At

Cee

Ctt

x

x

++−=

++−=

12ln

31

12ln

31

Page 3: Jawaban Tugas 1 Kalkulus 2

4. ∫ +++

22

2

)4(32

xxx

∫ ∫∫ +−+

+=

+++

−====

++++=+++++

++=

+++

dxxx

xdxdx

xxx

DCBA

DCxxBAxxxx

DCxx

BAxx

xx

22222

2

222

22222

2

)4(12

4)4(32

1210

)4)((32)4(4)4(

32

Cx

xxdx

xxx

++

+=

+−

++= ∫ ∫

41

2arctan

)4()4(2

2arctan

21

2

2222

5. ∫ +dxxx

x2

21

22 xx

xxx

x

+=

+

41

21

21

2xx

x

+=

ttt

xx

x

xt

subtitusi

222

2

41

21

21

41

+=

+

=

2+

=tt

∫ ∫∫ +−+=

+dt

tdtdt

tt

22

2Ctt ++−= |2|ln2

Cxxdxxx

x ++−=+∫ |2|ln2

241

41