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INTEGRALES
Anival Torre
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Integrales
Integrales definidosTeorema fundamental del
cálculoDescomposición de fracciones
parcialesIntegrales definidas
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Antiderivada
?6
:11
514
3
6
5
516
314
113
11 3
xxAnt
daantiderivaOtra
xxAnt
xxAntxAnt
1
1
n
xxAnt
nn
656 xx
72
7
5
31
32
78
76
54
2
7
3
7
7
5
33
xxAnt
x
xx
xx
xx
1 Formato de Integrales
derivada antiderivada
a)
b)
c)
d)
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Integrales
cx
x
x
x
6
86
26
66
6
6
6
cxfxdf
cxdx
La contraria a la derivada mas una
constante (c)
Integrales
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cxxx
dxsenxdxx
dxxdxxsenx
x
dxxgdxxfxgxf
cn
xdxx
nn
cosln3
2
11
1
23
21
1
Ej. de integrales indefinidas5
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xxdx
x
x
carctgx
arctgxdarctgx
cx
cx
dxx
1ln
ln
4
88
55
45
487
cxcx
xdx
dxdx
xd
x
dxxsenx
dxx
xsenxdxtg
seclncosln
cos.cos
1
.cos
.cos
1
.cos
1
.cos
dxdx
xdx
dxx
x
ln.ln
1ln
5
5
a)
b)
c)
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cffd
cxdx
dx
22
cede
x
iabledecambiounHaciendo
dxedxdx
dxe
dxex
dxex
Ej
xx
xx
3
1.
3
1
:var
.3
1..
3
1
.3
.
3
33
32
33
33
a)
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Teorema fundamental del cálculo
dxgffgdxgf
cxxx
dxx
xxxdxxxfdxx
ln
1lnlnln
cxsenxx
xdxxx
dxxxxx
dxxdxxsenx
cos
coscos
coscos
cos
b)
a)
Para aplicar este formato tiene que
haber una multiplicación o
darle la forma de una multiplicación.
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cxxe
cexexe
ceexxe
dxeexxe
dxexxe
dxexxe
dxxedxxe
x
xxx
xxx
xxx
xx
xx
xx
22
22.
2.
.2.
.2.
.2.
.
2
2
2
2
2
2
22c)
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cxx
cx
xx
x
x
xxxx
dxxx
dxxx
xx
2
1ln
2
2ln
2
1
1ln
ln2
1
ln.2
ln
2
22
222
2
2d)
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cxxx
dxdxxdxx
dxxxdxx
cx
x
xdxdxdxx
423
44
442
25
55
23
2
22
2
a)
b)
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c
x
cd
dxddx
ddx
xd
dx
d
x
dxx
4
2
4
1
2
2
2
4
43
3
c
n
xdxx
cx
xdxdxx
nn
1
33
10
5
555
1
10
99
c
xc
dd
xdxd
xdxdxdx
d
xdxxx
22
5
11
1
2
1
2.
2
22
55
211
1010
2102
a)
b) dxxd
c)
d)
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Descomposición de fracciones parciales
cxx
cxxx
dx
dxx
dxx
xxx
x
x
x
dxx
x
5ln7
5ln75
71
5
71
5
25
71
5
75
5
25
2
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cxdxx
cx
xdx
dxx
cdxx
5ln35
3
2ln
22
1
2
1
ln1a)
b)
c)
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Integrales definidas
2
1
0
21202
0
12
.2
.2
2
20
1:
u
eex
xdeex
dxxeex
dxex
dxexdxeSol
dxe
xx
xx
xx
x
xx
x
La int. Definida halla el área de una sección acotada
comprendida entre funciones.
Desaparece la constante
“c”
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2
2
1
0
514
0
13
32cos
ee
xxxsen
e
dxxxe
x
x
a) b)
4
2
2
1
4
1
4
1
4
1
40
1
dxxdxxdxxA
dxxdxgf
xy
xxy
n
c
m
n
b
m
c
a
b
adxxfdxxfdxxfdxxfdxxf
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20
1
10
15
100
1
10
15
5
15
5
2
2
2
2
xy
xy
xxy
xxyxf
1
5/3
1
35
0325
352
2
x
x
x
x
xx
xxx
2
32
232
2
1
5/3
75/94125
27
3
5
5
9
25
9
3
7
5/3
1
3
53
5/3
1
23
53
2
5/3
153
uA
xxxA
xxx
xA
dxxxxA
xdxfxgA
-3 -3/5
-1/100
1/10 1
3
f g =techoBase=
A esto opera lal int.
Definid.
y
x
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Gráfica de las funciones trigonométricas
22
3 2
1
-12
2
3 2 x
y
y
x
1
-12
2
32
2
2
3 2
Y = sen x
Y = cos x
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2
2
2
3
2
32
2
2
52
5
2
2
2
5
2
3
2
3
2
2
y
y
x
x
2
5
F(x)= tg x
F(x)= ctg x
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2
2
2
3
2
3 2
2
2
2
2
5
2
5
2
5
2
5
2
2
2
3
2
3
y
y
x
x
1
1
-1
-1
F(x) =sec x
F(x) = csc x
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2
2
1-1
Y= arcsenx Y= arccos x
Y = arctg x Y = arcctg x
1/2
-1 1
2
2
2
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Y= arcsec x
Y= arccsc x
x y
2
2
2
1-1-1 1
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Gracias
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