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