solucion evaluacion 2 mat215
DESCRIPTION
Solucion Segunda Evaluacion Matematica 2 FIA UES 2015.TRANSCRIPT
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1) 2 3(20%) 10 (5 )cos (5 )sen x x dx CLAVE 1
2 3 2 3
2 2
2 2
10 (5 )cos (5 ) 10 (5 )cos (5 )
10 (5 )cos (5 )cos(5 )
10 (5 ) 1 (5
4%sen x x dx sen x x dx
sen x x x dx
sen x sen
=
=
=
2 4
2 4
) cos(5 )
10 (5 )cos(5 ) (5 )cos(5 )
(5 ) 5cos(5 ) cos(5 )5
105
4%x x dx
sen x x dx sen x x dx
duu sen x du x dx x dx
duu u
=
= = =
=
3 5
3 5
5
2 2 = + C 3 52 2 (5 ) (5 ) 3 5
4%4%
du
u u
sen x sen x C
= + 4%
2) ( )(20%) 6 2 5x x x dx+
( ) 3 12 23 1
2 2
5 322 2
6 2 5 6 2 5
6 2 5
12 10 5 3
8%
6%
6%
x x x dx x x x dx
x dx xdx x dx
x x x C
+ = +
= +
= + +
3) 33 2 4 6(15%) 4 4x x x x dx + +
33 2 4 6 3 32 4 6
4 23 3
6
2 23
2
23
53
52 3
1 4 44 4
4 4
( 2)
22
1 23
103 ( 2)
10
5%
6%
4%
x x x x dx x dxx x x
x xx dxx
x x dx
duu x xdx
u du
u C
x C
+ + = + +
+ +=
= +
= + =
=
= +
= + +
1
-
4) 2(20%) ln( )w w dw Una forma
32
3 32
32
33
1ln( )
31ln( ) ln( )
3 31ln( )
3 31ln( )
3 9
8%
8%
4%
u w du dwwwdv w dw v
w ww w dw w dww
ww w dw
ww w C
= = = =
=
=
= +
5) 5
3 4(15%) ( 3)x dx
x +
( )
( ) ( )
3 3
2 2
5
3 4 4
3 4
2 3
2 33 3
3 3
33
3( 3) 3
1 33
1 16 31 13 36 3
5%
6%
4%
u x x ududu x dx x dx
x u dudxx u
u u du
u u C
x x C
= + =
= =
=+
=
= + +
= + + + +
2
-
6) (10%) ( )bxe sen ax dx
( ) cos( )
( ) ( ) cos( )
( ) cos( )
cos( ) ( )
( ) cos( ) ( )
5%
bxbx
bx bxbx
bxbx
bxbx
bx bx bx
bx
u sen ax du a ax dxev e dx vbe ee sen ax dx sen ax a ax dxb b
e asen ax e ax dxb b
u ax du asen ax dxev e dx vb
e a e esen ax ax asen ax dxb b b b
e
= =
= =
=
=
= =
= =
= +
=
2
2 2
2
2 2
2 2
2 2
2
2 2 2
( ) cos( ) ( )
( ) ( ) ( ) cos( )
( ) ( ) cos( )
( ) ( ) cos( ) 5%
bx bx
bxbx bx bx
bxbx bx
bxbx bx
a asen ax ax e e sen ax dxb b ba e ae sen ax dx e sen ax dx sen ax ax eb b b
b a e ae sen ax dx sen ax ax eb b b
b e ae sen ax dx sen ax ax e Ca b b b
o
+ =
+=
= + +
[ ]2 2
( ) cos( )
( )bx
bx
tambie ne bsen ax a ax
e sen ax dx Ca b
= +
+
3
-
1) 2 3(20%) 14 (7 )cos (7 )sen x x dx CLAVE 2
2 3 2 3
2 2
2 2
14 (7 )cos (7 ) 14 (7 )cos (7 )
14 (7 )cos (7 )cos(7 )
14 (7 ) 1 (7
4%sen x x dx sen x x dx
sen x x x dx
sen x sen
=
=
=
2 4
2 4
) cos(7 )
14 (7 )cos(7 ) (7 )cos(7 )
(7 ) 7 cos(7 ) cos(7 )7
147
4%x x dx
sen x x dx sen x x dx
duu sen x du x dx x dx
duu u
=
= = =
=
3 5
3 5
7
2 2 = + C 3 52 2 (7 ) (7 ) 3 5
4%4%
du
u u
sen x sen x C
= + 4%
2) ( )2(20%) 3 2 5x x x dx+ ( ) 5 3 12 2 2 2
5 3 12 2 2
7 5 32 2 2
3 2 5 3 2 5
3 2 5
6 4 10 7 5 3
8%
6%
6%
x x x dx x x x dx
x dx x dx x dx
x x x C
+ = +
= +
= + +
3)
33 2 4 6(15%) 6 9x x x x dx + +33 2 4 6 3 3
2 4 6
4 23 3
6
2 23
2
23
53
52 3
1 6 96 9
6 9
( 3)
32
1 23
103 ( 3)
10
5%
6%
4%
x x x x dx x dxx x x
x xx dxx
x x dx
duu x xdx
u du
u C
x C
+ + = + +
+ +=
= +
= + =
=
= +
= + +
4
-
4) 2(20%) ln( ) d
32
3 32
32
33
1ln( )
31ln( ) ln( )
3 31ln( )
3 31ln( )
3 9
8%
8%
4%
u du d
dv d v
d d
d
C
= = = =
=
=
= +
5)
5
3 2(15%) ( 3)x dx
x +
( )
( )
3 3
2 2
5
3 2 2
1 2
1
13 3
3 3
33
3( 3) 3
1 331 ln31 ln 3 33
5%
6%
4%
u x x ududu x dx x dx
x u dudxx u
u u du
u u C
x x C
= + =
= =
=+
=
= + +
= + + + +
5
-
6) (10%) ( )axe sen bx dx
( ) cos( )
( ) ( ) cos( )
( ) cos( )
cos( ) ( )
( ) cos( ) ( )
5%
axax
ax axax
axax
axax
ax ax ax
ax
u sen bx du b bx dxev e dx vae ee sen bx dx sen bx b bx dxa a
e bsen bx e bx dxa a
u bx du bsen bx dxev e dx va
e b e esen bx bx bsen bx dxa a a a
e
= =
= =
=
=
= =
= =
= +
=
2
2 2
2
2 2
2 2
2 2
2
2 2 2
( ) cos( ) ( )
( ) ( ) ( ) cos( )
( ) ( ) cos( )
( ) ( ) cos( ) 5%
ax ax
axax ax ax
axax ax
axax ax
b bsen bx bx e e sen bx dxa a ab e be sen bx dx e sen bx dx sen bx bx ea a a
a b e be sen bx dx sen bx bx ea a a
a e be sen bx dx sen bx bx e Ca b a a
o
+ =
+=
= + +
[ ]2 2
( ) cos( )
( )ax
ax
tambie ne asen bx b bx
e sen bx dx Ca b
= +
+
6