UNIVERSIDAD NACIONAL DEL CALLAO

MATERIA: MATEMATICA II

DOCENTE: NILTON SARAVIA

ALUMNA: CHAUCA SANCHEZ ANALIZ TATIANA

TEMA: EJERCICIOS

CICLO VERANO

2015

45) L: y=2 ; : y= 0 , x= 0 , y=2

Y

Y=lnx

y=2

1 x

V= 2 02 (y-2) (ey-0) dy

V= 202(y.ey-2ey)dy

V=2[y-ey-ey-2ey]02

V=2[y-ey-3ey]02

V= 2[2e2-3e1+3e0]

V=2[3-e2]

46) L: x= e3 , : y=lnx , y=0 , x=0 , y=2

Y

y=lnx

2 y=0

0 1 x

V=02[ey-e3]dy

V= 02[e2y-2e3-ey+e6]dy

V= [e2y/2 2e3e4+e6y]02

V=[e4/2-2e3.e2+e6.2-1/2 +2e3]

V= [e4/2 -2e3+2e6+2e3 1/2]

47)

4

Y=4-x2

-2 0 2

V=2 -22(x+2)(4-x3)dx

V= 2-22(4x-x3+8-2x2)dx

V=2[2x2-x4/4 +8x-2/3x3]-22

V=2[2(22-(-2)2)-(24-(-2)4/4)+8(2+2)-2/3(23-(-2)3)]

V=2[64/3]

V=128/3 3

48) y x=y

Y=

X=2

0 4 x

= [10 2] ( 2) ]

= [4 ( 4 4)]

= [4 4 4]

= [4 ]

= [42

3

2]4

0

= [8

3 4

] =

40

3

49) y

X=1 x=y

1 4 x

Y=-2

V= [(

2 ]

= [( 1

2 4 (

1

4]

= [ 2 1

4

4

4]

= [

2

8

3 8 2 ]

= [4 1

2 4 4

8

3 (4

1

)

8

3(4 1)

2(4 1 ]

= [(1

2 4

8

3) (4

1

) 8(2 1 2 3]

= ( 4 14

6)

y

50) x=yseny

0 15

x

= 2 ( 2 (

6 )

= 2 [

6

2

6 2 ]

= 2 [

6

2 2 2

3

2( ]

60

= 2 [

12 2 2

3

2 ]

60

= [

432

36 3

2

2

6

6 2

6

3(

3) 2

6

2

6

6 2 0]

= 2 [

432

3

2

6

23

2

2 (

1

2)

3

3

2

2]

= 2 [

432 (

3

2

1

) (

1

6

3

6) 1 3]

51)

0

= (

)

=

= (1

)

= [ ( ]

40

= [

4

[ (

4

4) ( ]]

= [2

2 [

2

2 1] ( ]

52)

Y

x=1

y=(x+1)cx

0 1 x

= ( 1

= ( 2 2

= [( 2 1

2

(2 2

4

2

8

]1

0

= [4

2

4

4

4

(1

2

2

4

1

4)]

= [

4 (

1

2

1

2

1

4)]

=

53) L: X=0

y

x

= 2

= 2

2

1

0

= 1

0

= [ ]

= [ 1]

54) x=1 x=3

V=213(7-x)(x.e2x)dx

V=213 [7xe2x-x2e2x]dx

V=2[ (xe2x/2 e2x/4)-(x2e2x/2 -2xe2x/4 +2e2x/8)]13

V= 2[ xe2x/2 7e2x/4 x2.e2x/2 +x.e2x/2-e2x/4 ]13

V=2[(21/2e6-7/4.e6- 9/2e6+3/2e6-e6/4)-(7/2e2-7/4e2-

1/2e2+1/2e2-e2/4)]

V=2[11/2 e6-3/2e2]

V=[11e6-3e2]

55) y=-1 y=lnx y=0 ,x=e

X=e

Y=lnx

1 e

= ([ 1] [0 1]

= [ 2 1]

= [ 2 2( ]

1 ( 1

= [ 2 2 2 ]

1 ( 1

= [ ]

1 ( 1

= [ 1 1 1 1]

= [ (1 1(0 ]

=