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# INTEGRAL Apostila (2)

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```RESUMO
Nesta Unidade tratamos o conceito de função primiti-
YD\ufffd\ufffdH\ufffdFRP\ufffdLVVR\ufffdFRPSUHHQGHX\ufffdWDPEpP\ufffdD\ufffdGHÀQLomR\ufffdGH\ufffdLQWHJUDO\ufffd
LQGHÀQLGD\ufffdH\ufffdVXDV\ufffdSURSULHGDGHV\ufffd\ufffd\$SUHQGHX\ufffdD\ufffdFDOFXODU\ufffdR\ufffdYDORU\ufffd
de algumas integrais imediatas, bem como a calcular uma
LQWHJUDO\ufffdGHÀQLGD\ufffdDSOLFDQGR\ufffdR\ufffd7HRUHPD\ufffd)XQGDPHQWDO\ufffdGR\ufffd&iO-
FXOR\ufffd\ufffd9RFr\ufffdWDPEpP\ufffdDSUHQGHX\ufffdDOJXPDV\ufffdWpFQLFDV\ufffdGH\ufffdFiOFXOR\ufffdGH\ufffd
integrais e de integrais impróprias.
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322
RESPOSTAS
Exercícios propostos \u2013 1
1) a)F (x) \ufffd 5
3
x3
7
2
x2
2x + K .
b)F (x) \ufffd < 4 x
<
1
4
K .
c)F (x) \ufffd < 2 x
<
1
2
K .
d)F (x) \ufffd ln (x <1)
K .
e)F (x) \ufffd e
4 x
4
K .
2) a)F (x) \ufffd <2cos x
sen x < x
3
6
K e K \ufffd /
3
384
.
b) F (x) \ufffd 3 x
1
3
x
2
2
K eK \ufffd <3.
c) F (x) \ufffd sec x
sen x
K eK \ufffd < 3
2
.
d) F (x) \ufffd 3
7
x
7
3
ex
K e K = 1.
e) F (x) \ufffd senx
cosx
K e K = \u20131.
3) a)
x5
5
< 8
3
x3
16x
C .
b) ln x
6 x
1
3
C .

c)
x4
4
< 4
3 x
3
2
< 3
x
C .
d) 4x < x
2
2
< x
3
3
C .
e) < 1
2x2
C .
\u2022
Módulo 2
323
Exercícios propostos \u2013 2
1)
33
2
.
2) a)
/ 2
8
1; b) 21
4
; c) 1; d)e2 <1.
Exercícios propostos \u2013 3
1)
1
5 7 - 5x\ufffd 	2
C . 2) <1
x
C .
3)
1
7
sen 7t < /\ufffd
C . 4) <1
6
1< 2x2\ufffd
3
2
C .
5)
3
3
arctg
x
3
C . 6) 1
4
.
7)
5
2
= ln 4\ufffd 	2 . 8) 10 <1.
Exercícios propostos \u2013 4
1) exx2
ex
C .
2)
1
3
x3 ln x < x
3
9
C .
3)
2
3
x3/ 2 ln x < 4x
3/ 2
9
C .
4) < 1
2
cosx sen x
x
2
C .
5)
1
2
ln x\ufffd 	2
C .
6) <xe<x < e<x
C .

Exercícios propostos \u2013 5
1) 2 . 2)< 1
4
. 3)
/
2
. 4) . 5)' .
\u2022
\u2022
\u2022```