.1 P I'I' M IH IH I
JjOt~
/I
0,0
AI
I,
~,l1
7,OO7~,
,S 0,41
,SOOll
4,7
0,0887
4,0
,6 0, 0,7 0,
0,3060 0,4892 0,6433 0,7769
1,,112111
1'l,1
0,
2,1072 2,2088
1,50 1.5892
9, 9,
2,2300 2,2407
~()41
1,IH7f1
5, 5,
1,6864
9,9
1,7228
11
1,0 1,1
0,0000 0,0053
j,,8
0,2624 0,3365
5,8 5,9
0,4055 0,4700 0,5306 0,5878 0,6419
6,0
1,7918
6,2 6,3 6,4
1,8245
1,5 1,6 1,7
1,8 1,9
2,0
2,
2,2
0,7419
6,6
2,
1,9169
2,4
2,7 2,8 2,9 3,0 3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8 3,9 4,0 4,1 4,2 4,3 44 ol
TABUA BU
DE INTE INTEGRAl
CERTAS F6RMULAS FUNDAMENTAlS
2,2513
5,5 5,6
l.4
~HIIill ~HIIill
I, 'b
(1,'1
0,0
O'
15 16 17
30 35
1,1314
7,6
1,2528
8,0
1.
2,3026 2,3979 2,4849 2,5649 2,6391
2.
2,9957 3,2189 3,4012 3,5553 3,6889
2,0015
60 65
2,0149 2,0281
.10 75
4,2485 4,3175
85
4,4427
100
4,6052
2,0794 2,0919
8,9 ad
(X)
f[J(X)
g(x)Jdx
ff(X)dX+jg(X)dX
uv -.fV -.fVdU dU
un+l
o-
6.
;6
cos u d
8.
sen
(ax
0,1'
y;
aUdu
(b)
du
(a)
7.
9.
2,1401 2,1518 2,1633 2,1748 2,1861
dfd~X»)
af
C,
;6 1,
a>
en
du
cos
EXPRESSO ESSOES ES
2,1163 2,1282
1.4816
3.
c.
(X dx
2,7081 2,7726 2,8332 2,8904 2,9444
3,8067 3,9120 4,0073 4,0943 4,1744
50 1,0296
2,2121 2,2824 2,2925
b)ndx
(ax
QU
ENVOLVEM LVEM
b)n+1 (n
J)
ax
b,ab
.;6
C,
n~-I,-2 ir
al
APENDICE
A1
lax
2"
ll
APENDICE
bl
[ax
/'--)n+2
1;) dx
Vax
11.
11
11.
b)- dx
13.
lax
bl
_]+C,
14.
ax 2b 'n
0-
11.
-4 -0
11.70-2,
(ax
16.
x+
b)- dx
(x2(ax
_L ax.+b ]+C (Se 11.
dx
[(ax
b)
lax
2b
'2"
o.J
7.
(ax
b)-3 b)-3 dx
dx (ax
l8.
21
=l_L[-'X_[+C ax
b)2
=b2L
dx x2 (a
1. ~;2 (ax
ax
ax
b)
dx
.20,
a3
1;)
bl
(ax
28.
-4
Vax
dx
s.
!_
'bx
se
= , , , -
-2
) t\t\ -
Vb
d» oV
.V
I~,
I-
(a
'I"
JIINVOI,Vlil
I- )1 11
lI,n II
II"
(I,
Ii,
1,
-I, IIII
IIM!I
v'tiJI
~f
V~_
(~:I
N,Il IH
/J
bw
I -
()
.1,
,1,1 (I,
1 1 ,1 ,1 ' ( I I ~
/11,
II
+,0,
vax+b+Vb
-1-.£.1
II
Il1
(1,11
ax
b
l~
11
(f.l ( ,j,j l/l/ jljl l
1,
Jax
rg coth coth
_l_L (ax -I-
ax
se
29
l ilil t
ax
argt
Vb
[a.'t.+
b/
b)'1
17b.)
xvax
Il (ax
. > 1 ; s e 11
2V-ax-+-b
+C
11.
I~,t llll jqjq H l
us
dx
(a)
(b)
b)2
b)!l
ax
-2
(,
x~
+0
el
~+o
w V a : v -I-
b>
/J
A12
APENDICE
APENDICE
32
!_ argth
34.
C,
se
<.1,
C,
Be
~+
43.
2)n
(Va
X=
x2)n+2
=_!_Llx+a[+c 2a
• /
44.
45.
V~ "la
47. -x
48. 38.
dx
!_ argth
-=--
se
C,
1-=--1 se
2)
.2
dx
Va
39
dx
Va +x
argsh
QU
-=--
I:I>
dx
"2
argsh
ja
+x2= xVadx
V~
-=--
\~I
1,
a>
Va
args args
.1,
ENVOLVEM
lx
/~+
V~+C
E X P lU lU l JS JS a O llll i s
EXPRESSO ESSOES ES
-2
aargSh[
+x2d
Va
,n
0;21
~Jd:t
-r.----iI
n -
$I
~~
Va
--
a~
I'll.
1Il1.
Q U I D : ro ro N V O LV LV l lJ lJ M
n -
III (£
A14
APENDICE
APENDICE
_x )2-n (n
(n
2)
2)
"" -2 67. ·/
.,55
dx"=
va
xl.
8"
dx
2 -
"8
- x (a - a
68.
69. va
57.
dx
X2
Va2-x2
arg
x2
arg ch
a2
dx
aarr se
_!
el
va
arc
_£
vx
Va
_!
s.
ar co
+0
ax 59.
vx
h -
n-
70.
58.
dx
dx EXPRESSO ESSOES ES
ENVOLVEM
sen( arc sen(
72.
60.
QU
x -
];2
73. arg.ch _£ +C
62.
j"
dx
!£
_£
_a )n
Vx
[z
ar
74.
se
(..!..::.l!..)
()
x 2 ) n dx
(V~1)"
ch _£
na
!£ aarr
dx
(v
I II I I ', (/',1'
. InIn .1.1 1
,1
tlill
,Ii/\
~)
II
A16
A17
APftNDICE
'77.
'f
dx
sen n +
ax
(n
cosax dx sen ax .J
c s n -
dx xV2ax-x
80.
EXPRESSOES
81.
sen
82.
cos
1~~
TRIGON IGONOMETRICA RICA
QU
sen ax
ENVOLVE~J: E~J:
93.
sen ax
sen"
l(
94.
86.
os"
(a)
na
--
ax cos'"
m~
sen" ax cosm- ax dx
m~
sen
~n
ax
n)
,m
+n
--
--
sen
cosn-
dx sen ax
96
-1
Ie
sen ax
V~ sen ax
cQs axl"\- C, n~
(b)
ax
01
ax
95.
ax cos ax
cosn-l ax sen ax
ax cos b x d x
(I
a(
na
l=
iJt,,,
ax
4a
-senn-l
()
eo
sen 2ax
cosaxdx
en"
n~,
C,
[cos [cos axl
sen +! ax'c ax'cos os
4a
85.
cosn+! ax 1) (n
sen" ax cos'"
sen2ax
84.
dx
sen"n-:-lxcos (m n)
><
~-
sen axl
cos" ax sen ax dx
senax cos
cos ax
83
I'IH.
91.
a:
1)
cos (a (a
b) b)
sell bxdx
sen, (a
II
bx dx
sen (a (a
b)
OG
( IrI r Q ( I
(a
b)
cos
sen (a (a
(a
(a
)x
(a
b)
(12
b) x,
b) b)
)..
II
0,
11~
A18 lix
lOO=~-=L
bcosax v~senaxl b+ccosax
ax
0/
dx
ax
cos ax
103.
-r:
sen
COB
105.
sen
106.
ax cotg -2 . ; ; 1 : .
sen
104.
113.
sec
Isec Isec ax
114.
cosec
lIS.
sec
116.
cosec"
117.
seen a x r l
?"
cos ax
-2
f'
118.
cos
tg
ICOB
ax dx
110.
ootg
ax,,8t)C
ax,
QU
c o e c ax,
F-
ax
121.
f'
ax dx, (So
"o',..tI " o
seen ax
en 1, use C0.'3ec
na
ax eotg ax
,O
=-
eose,e ax na
..L
I,
to,
s e N.o
QU
ENVOLVEM
FUNgOES
se
.O
nr"O
aarr se ax
22.
aarr co
aarr co
123.
ar tg
a r t g ax
+!
xn
aarr se
x"
( 11 11 '
OQ8
(v
111'0
tit
xnIl
'n+l
107.) fI
II
TRJ:GClNOMETRICA
INVERSAS,
a;
- 2
1-
yIl--2? 1x-
.i 2a aarr se
ate
l'
(1
os ax -I-
t~ ( 1 . 1 1
a,
dx VI '7u :1;n'H
X-
nn
1"11 71
n,A
m , v l , 1 ,I
V1 ~~~ r I , ' ,U »,I
113.)
ax x,
C,
-
aarr se
j' n-2
+,,--
coseen- ax cotg ax
seen ax tg
EXPRESSQ ESSQES ES
tg
tgn-Iax 1) a (
1)
a(
ENVOLVEM
cotg
:c
secn-3 ax tg ax
cosec"
119.
Lisen ax
l'
otg ax
=-
(Se
senax
TRIGONOMiTRlCAS
'tg ax, cotg
tg2
('
(Se
cosec"
109.
cotg axl
tgax
sen ax
xn sen
EXPRESSOE
108. fcot
[cos [cosec ec ax
=-
os ax '+.,
ax
-;;COB
xn cos
107:
tg axl
'I
dx
lQ,I2,
19
APtNDICE
APENDICE
'II
11 ,)
A20
APENDICE APENDICE EXPRESSOES SOES
QU
ENVOLVEM,E EM,EXP XPONENCIAI
LOGARITMOS
a~O
-+
8h 2a.x 4a
142.
128.
_!
dx
/;a"
'hn
143 129.
xe
--;_;2
dx
sh
ax ell
n -
ax 8h ax
-~
f.
ax
sh
0,
_J_
eax
A,21
ax
ch
(X
na
eh
f-
t .
dx
n~O
1)
sh ax :c
eh
:<
a-
eh ax -+
145.
eh
sh
146.
sh
147.
xn eh
148.
th
149.
cothcz dx =,~
axl -+
150.
th
ax -+
151.
coth" a:c
oth ax
_£
sh ax
0,
sen
132.
cos b.x dx
33
134.
(1:2:
135.
xn
136.
X~l
lS7.
;Lax
-=
dl;
, ; . ,
bo
a-
e=
,be a-,,-
sen
- b cos
(a cos bx
0'
ax dx
xn+1
sh
x -
(eh ax)
in.
'2
ax)2
ILaxl 152.
JC
eh -a dx
x -
"en u· "x)
n+
=-
r'
39
;- eh
dx
dx
11
xn
-C
ax dx
;; ch
ax
' MFU MFUN<;O N<;OIC IC
Hll'ER Hll'ER
LICA LICAS,
":": ":":
-1-'!th
hn-1ax
(n
1)
al''1lx,
It
(S 11)3.
!_ sh ax
Ii fl.G
/I,
coth
Goth" ax d :J J
it
ni
11
..!.
( t: I
II,n
Ii
1)
ax
(Iill
r,
II.iI II,"
,/0" coth'l-D
1,
WI
I,
IIH!\
e lm ,
N,I'
111),
A22
156.
Al'ftNDICE
seeh axdx
th ax
eot1l ax
ax dx = -
158.
seoh=? ax th
_ : : _ : : . . : : _ - - = = - - = - - - =ax =-
sech" ax dx
--
1)
(n
sech
ax dx
(Se
I,
iNDICE ALFA ALFABE BETIC TIC
n;;o!l 1M.)
(O
159.
co se
ax
co-sech
d.
ax coth ax 1)
(n
entr n 'i'i ltlt me me ro ro s entr
pal' pal'cn cnte tesi si
co-sech'"? ax dx
n-
l e a ea o
160.
sech"
ax ~::":':'_::::::"'+c,
eeh" ax th
Allen,
nr"O
na
. D. ,
161.
o-sech" ax e6th
162.
ax sh
co-sech" ax :':::"'::'::":::'::_~+c, na
Convergencia
bX
e=
bx
duas duas curv curvas as
ax ch o x t l
e a [ ebx
C,
e- bx
INTEGRA EGRALS
e- dx
164.
(n)
(n
de inte integr grai ai Coordenadas,
impr improp opri rins ns
o la la r s ,
Cos (A ICos 08 (1 ), (1 Cos 2A Curva(s)
coord. coord. polare polares, s, 30 da f'uncfio, entr entr curv curvas as 23 pelo a l u l sob 192
C us us t
206
263-
m a g in in al al ,
Degr Degrau au
e tc tc .
fun< fun<;ao ;ao
Delta-z, tox, 17 Delta-s, toy, 17
;»
Deseontinuidade, 165.
166.
co
e=
x'
sen"
J-
dx
a um um el el , W . T. '30 R.
Buck,
dx
cos"
dx
1·3·5···(n-l)
se - 44- 6
da
de
7r
2'4·6· "n
(n
Culculo, dif' dif'or or
:1
ur
----n'n;(\[j'l'1'h,,-;l{)._ lilt 1 :1:1 1 1' 1 [,[, 1 1 1 1' 1 1 1 ' I I (111t11fll'IIlHlIILo
dn
I) \ lt 11 11 I
II11] (L
(1
' ru ru ' J~ J~ I1 I1 ( '
de
ac
t b~ b~ ' < 1 0 R O m lt R
I 1 ng n g u ltlt 1 ,1,1 '
M l' V( \
( \1 1 1
(\
(llll'VIl.
I'!
(1
1 ," ,
(1 (1
1b
' j J r . {II'!
11(1 ~;: ,a(1 ~b/ll, li
In
I'
14
ilJ,
70
20
' t r 'i g o n o m 6 t l ' l
L r
30
onh6ic onh6icle, le, 27
O o ' C iC iC ' ioio l l
into intoil il'o 'o Impa Impa
51
as, 821,
l()8
!I,
50
fUTI()flcH
22
ncia ncial, l,
nrdioido,
1)
7C1~,
httl 29
15
fun~1to uroa, u, 18
1 1 l ex ex "
intq4'l'fll,
intei inteiro ro pal' pal' ': 2,
4,(1)
97
derivada
C,
DEFIN DEFINIDA
I)!,
03
Apostol, Area, compri comprime mento nto 25 co lar 30 Area, como como limi limite, te, 19 calc calcul ulo, o,
163.
10
"psi "psi", ",
nr"O
90
u ni ni f' f' or or m
A1neTicqn
Angu Angulo lo entr entr
i1'I,d'i(}{tdrkll)
l}(igina8
Continuidadc, 85 d o s om om a p ro ro d t o c oe oe ie ie nt nt c diferenciabilidade, 90 ordinaria uniforme, 93
(Se
n;;o!
na
problemas,
('HI
l.'tloJ{)1l0;lfl,
:r
I'!O
ttl
INDICE ALJe'A ALJe'ABlh BlhICO ICO INDICE ALFA ALFABE BETIC TIC
de
mais reg ra
de
variavcl,
de,
12
74
a de de ia ia ,
un go go e potsnciaa- d e f un cas, 370 potencias
Dif'erencincfio
umero
racional,
tmmb6m
'(uCT
irracicnal, 43 (5)
43
«(J)
rea.l,
56
raeional,
(11)
f/~-,
co-senos,
37.6
.53
segunda,
r ig ig on on om om e r i
Num
t('I~,
Diferencial,
a,
lo
nt Distancia,
(9)
de
Limite(s)
182
B ri ri ta ta nn nn ic ic a
P ar ar c a l e ut ut e
(8)
c on on titi nu nu a
fUll~i'iO,
2:l7
propl'ieclades,32
Equacoes
Log.
Es
Integral
Integracao)
du
de COS1~ do cos"
aU
&/0,
63
fun~1io, E nc nc yc yc lo lo pa pa ed ed i
103
J.,
Implicita,
\;
trajetoria,
'n
,."Fra ,."Frar;o r;oes es
J.
Ortogonal,
Dominio,
",ij~~~at,
Olmsted,
p rl rl nf nf ~J ~J Q' Q' :d :d e pl{TCl pl{TClat~ at~;.' ;.' gS8
1 38 38 '
a,
89
.,1'€)~';IZ·ii,l(a'-+u'), >S:~,~,;.,1'€)~';IZ·ii,l(a'-+u'),
lladiano
38
r 7 -
du/ 1),2, d1,/ V;;2~2, ax
3405
~, 352
380 382
cos
397 du, :i89
11
c t d o
UID!L,
426
gr d!eo c1 um
:tnlll'Oll'1('I1'to Hn)HI~llr 207
ao
10(,f~ 11,
11m
oQ'!vl 1 ,], ] 1
Momentos,
Sears, 3G B eg eg u d s d e i va va da da , 5 1 equl1fl equl1floes oes pural'llula'l\J(tR, R i
(1,
"dsgl'au",
cxpcnenctal, "gamma",
bx -I-
ax
eorrespondgncin,
21
(16B)
aplic!tr,oes, do :funglles (1],
umn,
I H \ 1 1 1 1 '1 1 .1.1 , flIlT
(VOl'
175
4:115 ' t ,a,a m , b a m In Ii ~t"'l)
plan planet etar ario io
4.00
M, lA 'Ina.(l:Plnl~"" lO ~1'~III'(ln(1tn,Glto, 1'~I')l11'11M, II l'I'H(jMI';l PII"'I iiI H) l i M O :I lit! II I o t !
~('n (l(1'f'tIlic1o,
Movimento
(A-I-Jl,
'Son SOli
flO,I,
N.a.p.i~ N o, o, tU tU J'J' ul ul , l og og nX nX ''H Hmo
wton, S j mOco(lo y , O , 107
82
(,t-S
( . \ .l.l Y . f m l ' I I ' 870 170
:1:1)"
{iJ,170
SI.Il!lld SI.Il!lld a V l l ) ; Ull 1(1(111, 'I,~() SiMl 1.,( (1 1/1/1(1(111,
E l t n l 1 . 1 1 , ;0. f:111
1.1,
1\
Oil,
IIIU
M7
U~
~.-.-c"'''''
~ --\\ "r "r .
'\
'F
.I
\,
INDIcE -ALFABlhrco
.2
'I'r 'I'rap apez ezio io (3,
Tg
coni conicas cas 107( 107(38 38 normal (nor (norma mais is ), 100
instantanea,
'I'axas
114
etc.,
mx
sen
38
'l'urnbul~,
ol
Von
ra al rt
e(s) e(s)
23
revolucao,
23
1'
IV cierstrass,
ci in,
s,
30
relacionadas,
apli aplica caco coee
'I'rajctor
regr regr
'I'rigonometricas,
103
fu
as
-r»:
90
al
,.
'fiX
.,
I,
-
--.-----------~-= ClEN ClENTR TR
DE lENS lENSlN lN
TECN TECNOU OU'X 'XHC HC
",
1-
..
- ~ . . _ - .. ""'. .
~.
..., ....
~~
