CALCULO INTEGRAL
EJERCICIOS
PRESENTADO POR:
CHRISTIAN CHARRIS QUINTERO
DAVID DUARTE NUÑEZ
JAIME CAMARGO RANGEL
PRESENTADO AL PROF:
IVAN BLANCO
UNIVERSIDAD DE LA COSTA CUC
FACULTA DE INGENIERIA
2015-2
12:24
∫−1
2
x3d x
= x4
4 2 2−1 =14 (24−(−1¿4)
=14 (16-1) =154 +c
12:32
∫0
π
(senx+2¿eπ)dx¿
=-cosx 𝛑0 +2ex∫0
π
❑
=-(cos 𝛑 – cos 0)+2)pπ−20=-2+2(eπ−1¿=2+2eπ-2=2eπ+c
12-40
∫0
1ex
π+3dx
¿ 1π+3∫0
1
ex dx
= 1π+3
ex∫0
1..
= 1π+3
(e1−e0¿
= 1π+3
(e1−1¿
=e1−1π+3
12:48
∫1
4
√x+ 1
√x dx
=∫1
4
√x+∫1
41√ x
=∫1
4
x1 /2+∫1
4
x−1 /2
x3 /2
32
∫1
4
+¿
x1/2
12
∫1
4
¿¿
23(43 /2−13 /2 ¿2+2(41 /2−11 /2
=203 +c
11-30)
∫❑e√2dx
¿∫❑e
122
= e
122
11-40) ∫❑(x2−5 x+6)
x−2( x−2)(x−3)
=∫❑( x−2 ) .(x+3)
(x−2)dx
=∫ x+3dx
=3∫ x dx
=3(x)+C
11-50) ∫❑ tanxsenx secx+cosx=∫ senx dx=cosx+c
=
senxcosx
sen7x .( 1cosx )+cosx❑
=
senxcosx
sen2 x+cos7 xcosx
= senx
11-60)
∫ 1
√1−x2dx+1−x2
∫ 1
√1−x2dx+1∫ dx−∫ x2d x
arcsenx+x−13x3+c
f ( 12 )=ArcSen(12 )+12−13+c12=30+
12− 124
+c= 1124¿
¿
=73124 +c= 1124
C=1124−73124
=30
11-70
sif ( x )= x2−3 x+1x
fX)=1
f ( X )=(x2−3x+1)¿F(e)=1
∫ xdx−3∫ dx+∫ x−1dxF(e)=1
12x2−3 x+0+cF(e) =1
F(e) = 12
(e ¿¿2-3(e) +c = 1
11-80
si f(x) = 2sech2 x y f(o) =3 hallar (-ln2)
2∫ sec h2Dx
=2tanh x + c f(ln2)=2 tan h(ln2)
F(0)= 2 tan h(o) + c = 3
2(0) + c=3
C=3
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