Download - MATEMATICA II.pdf
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UNIVERSIDAD NACIONAL DEL CALLAO
MATERIA: MATEMATICA II
DOCENTE: NILTON SARAVIA
ALUMNA: CHAUCA SANCHEZ ANALIZ TATIANA
TEMA: EJERCICIOS
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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]
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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]
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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
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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]
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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]
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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 ]
=