Actividad 1 - Calculo Integral - Luis Felipe Cobo Canal - 2

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU

GKGVEBEBJU

=.

 Mprjxbimebõo  Mprjxbimebõo Ouiârbe Ouiârbem; m; gh ejstj imrabomh ng hm biprgsbõo ng uo emrtgh, ne 6 5  x eumonj sg biprbigo  emrtghgs, gs nx 9∛  x + = + 7 ∛  x Pmrm emheuhmr gh muigotj ngh ejstj gotrg prjnuebr =0 emrtghgs y 60 emrtghgs, sg ngfg emheuhmr hm sbaubgotg botgarmh; 60

∣ ∛  x x += +7 ∛   xx nx 5

 M9

=0

Emheuhg hms suims supgrbjrgs W y hms suims bolgrbjrgs H, tjimonj uom pmrtbebõo ng = uobnmn y prjignbg mifms suims pmrm nmr rgspugstm mh gkgrebebj. ( Mspgetj ( Mspgetj m gvmhumr; #= mprjxbimebõo ng botgarmhgs.) UJHWEBJO; 60

∣ ∛  x x += +7 ∛   xx nx 5

 M9

=0

=- Mphbemijs Mphbemijs hms prjpbgnmngs prjpbgnmngs ng ng hms botgarmhgs botgarmhgs jftgogijs; jftgogijs; 60

60

∣ ∛  x x += nx+∣ 7 ∛   xx nx 5

 M9

=0

=0

6- Umemijs Umemijs hms hms ejostmo ejostmotgs tgs y rggser rggserbfbij bfbijs; s; 60

60

∣

 M9 ( x + = ) =0

5- Uust Uustbt btub ubij ijs s   x + =9 y    M 9F + L   Ejo;

=/ 6

∣

=

nx + 7  x 5 nx =0

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU 60

60

∣

F9  y

= /6

nx  

∣

= /5

 L 97  x

y

nx

=0

=0

>- ^jimonj ^jimonj ejij fmsg fmsg hm Geu. Geu. 5 ng hm hm auém ng ng gstunbj gstunbj ng hjs ejoegptjs ejoegptjs físbejs, rgmhbzmijs hm botgarmebõo ng F; 60

∣

F9  y

= /6

nx

=0

F9

 y = 6

= += 6

+ E = +=

7- Ug rgmhbzmo rgmhbzmo hms jpgrmebjogs jpgrmebjogs ogegsmrbms ogegsmrbms pmrm pmrm sbiphblbemr sbiphblbemr hm gxprgsbõo gxprgsbõo;;

F9

 y

5 6

5

+ E = 

6

 y

5 6

=

F9

5

+ E = 

6



 x

=

 L 97

+ E 6

+ E 6

> 5

 L 97

 L 9

()

(   )+ 5 x

> /5

>

E 6

=7 5

>  x + E 6 ∛  x

5

4- Wom vgz vgz goejotrm goejotrmnms nms hms prbib prbibtbvm tbvms s tgogijs tgogijs qug; qug;  M 9F + L   M 9

6

=7 5 > 5  x + E 6  x + = ) + E =+ ∛  x ( x ∛  5 5 6

2- Msui Msuibg bgon onj j qug; qug; E 6+ E =9E   M 9

6

=7 5 > 5  x + E  ( x  x + = ) + ∛  x ∛  5 5 6

=0- Prjegngijs m emheuhmr hms suims ng meugrnj m hj nglbobnj go gh goemfgzmnj ngh gkgrebebj;

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU o9=0

 H M 9

 p ∌ xb   ∝ 9 b

W   M 9º

=0 =07,= =

 pb

== ==2,> 7 ==2,> 7

qb

 M 9

6

=6 =5>,6 1 =5>,6 1

q ∌ xb º ∝ 9 b

b =

b =

 x

o9 =0

=5 =>2,7 7 =>2,7 7

=> =,4 5

=4 656,= = 656,= =

=2 6>2,1 7 6>2,1 7

60

6 5  x + = ) + ∛  x  x + E  ( x ∛  5 5 6

Ejo ∌ xb 9 =  H  M9º

o9=0

∝  p ∌ xb9=1>2,- Ejo fmsg go hjs motgrbjrgs vmhjrgs emheuhmijs ∌ x b ∌ x =9 x =∖ x 09∖0,7∖(∖6 ) 9∖0,7 + 69 =,7 ∌ x 69 x 6∖ x =90 ∖(∖0.7 )90 + 0,7 90,7 ∌ x 59 x 5∖ x 69= ∖09 =

7- Pjstgrbjrigotg rggiphmzmijs hjs vmhjrgs gsejabnjs pmrm  x  go l ( x ) l  ( (∖= ) 9

( ∖= ) 5

+ ( ∖ = )9

l  ( ( 0,7 )9

(∖0,6 )5 5

( 0,7 )5 5

∖= 9

∖=∖5 ∖ > 9 9∖=,55 5

5

5

l  ( (∖ 0,6 )9

∖=

5

+ (∖0,6 ) 9∖0,606<

+ 0,7 90,7>=<

Ug tjimo hjs vmhjrgs go pjsbtbvj

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU

5

=

> 5

Ejo E 9E =+ E 6 7 >

2

> 5

|

∑ x ∖  x + E  = >

6

0

+ E 

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU

Gotjoegs tgogijs;

( ∑( ) ∖ ( ) )∖( ∑( ) ∖ ( ) ) 7

=

>

7 >

∖

 2 =0

>

2 6

9

>

=

5

 7

>

=0∖ 5< 4

0

>

2 6

>

0

5

9∖5.67

5

f)

  ∣ ( x x + x= ) ( x x ∖5 x ) nx 6

=

UJHWEBJO; Prjegngijs m mphbemr hms prjpbgnmngs ng hms botgarmhgs msé;

5

∣ ( x x + x= ) ( x x ∖5 x ) nx 6

=

( x + x∖ )(  x ∖5 x ) =

6

 Mphbemijs  Mphbemij s hm hgy nbstrbfutbv nbstrbfutbvm m ng hm iuhtbphbeme iuhtbphbemebõo bõo 5

∣ x ∖5 x + x ∖5 nx 5

6

=

 Mphbemijs  Mphbemij s hms prjpbgnmng prjpbgnmngs s ng hms botgarmhgs botgarmhgs

∣ x =

5

5

5

5

∣

6

5

∣

∣

=

=

nx ∖ 5 x nx +  x nx ∖ 5 nx =

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU  x

>

>

+ E =∖

(

5

 x

)

5

5

+ E 6 +

 x

6

+ E 5∖( 5 x + E > )

6

^jimonj qug E 9E =∖E 6 + E 5∖E >  x

>

>

S

 ( 5 )> >

5

=

|

=

∖ x5 +  x 6∖5 x + E  5 6

=

YS

6

∖( 5 ) + ( 5 ) ∖ 5 ( 5 ) ∖ 6

4= >

 (= )> >

=

∖ ( = )5+ ( = )6∖ 5 ( = ) 6

2

=

=

6

>

6

∖61 + ∖2 ∖ + =∖ + 594

π 

e)

  ∣ >sbo ( x6 )∖5ejs ( 6 x ) nx 0

UJHWEBJO; Prjegngijs m mphbemr hms prjpbgnmngs ng hms botgarmhgs msé; π 

∣

 M 9 >sbo 0

π 

( )∖∣  x

6

5ejs ( 6 x ) nx

0

Ub nglbobijs qug;  M 9F ∖ D , ejo π 

π 

0

0

∣ >sbo ( x6 ) nx D 9∣ 5ejs ( 6 x ) nx

F9

Bobebmijs fusemonj hm prbibtbvm ng; F π 

F9 >

∣ sbo ( x6 ) nx 0

=

=

6

6

Uustbtuygonj; u 9  T u 9  x ngrbvmijs  π 

F9 >

∣ sbo ununu 9 =6 nx 0

Y

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU π 

F 94

∣ sbo u nu 6 nu 9nx 0

π  F94 (∖ ejs u + e ) 0

( ( )+ )| 9∖ ( )+ | 9∖ ( (  )∖ ( ))

F94 ∖ejs

F

F

|

4ejs

4 ejs

 x

E  π 

6

0

 x

E  π 

6

0

π 

ejs 0

6

F9∖4 ( 0∖= ) F9 4

  π 

∣

 D 9 5ejs ( 6 T  ) ) nx   0

π 

 D 95

∣ ejs u nu6 0

 D 9

5 6

π 

∣ ejs u nu 0

5

|

 D 9 sbo u + E  π  6

5

0

|

 D 9 sbo ( 6 T ) + E  π  6

5

0

 D 9 − ( sbo ( 6 π )∖sbo ( 0 ) ) 6

5

 D 9 − ( 0 ∖0 ) 6

 D 9 0

W 96 T ngrbvmijs nu 96 nx

 nu 6

9nx

 

Luonmigotjs ng Eíheuhj Botgarmh - Ejoegptjs Físbejs ng Botgarmebõo Hubs Lghbpg Ejfj Emomh Eõnbaj; =.==7.011.520 ^ÂEOBEM PVJLGUBJOMH GO JPGVMEBÕO NG G]WBPJU BONWU^VBMHGU R ME^B\BNMNGU IBOGVMU

R nmnj qug  M 9F ∖ D   M 94∖ 0 4

 M 9