Tablice Izvoda Integrala Trigonometrija
2
Tablica izvoda: Funkcija ( x f Izvod (x) f ′ const c = 0 x 1 α x 1 - α αx x a a a x ln x e x e x a log a x ln 1 x ln x 1 x sin x cos x cos x sin - tgx x 2 cos 1 ctgx x 2 sin 1 - x arcsin 2 1 1 x - x arccos 2 1 1 x - - arctgx 2 1 1 x + arcctgx 2 1 1 x + - Površine ravnih figura: = b a dx x f P ) ( , ′ ⋅ = 2 1 ) ( t t t dt (t) x t y P , = β α ϕ ϕ ρ d P ) ( 2 1 2 . Tablica integrala: + = c x dx c n x dx x n n + + = + 1 1 + = c x x dx ln + = c e dx e x x c a a dx a x x + = ln + - = c x xdx cos sin + = c x xdx sin cos c tgx x dx + = 2 cos c ctgx x dx + - = 2 sin 1 2 2 1 1 c a x arcctg a c a x arctg a a x dx + - = + = + , 0 ≠ a c a x a x a a x dx + + - = - ln 2 1 2 2 , 0 ≠ a c a x x a x dx + ± + = ± 2 2 2 2 ln , 0 ≠ a 1 2 2 arccos arcsin c a x c a x x a dx + - = + = - , 0 > a c x tg x dx + = 2 ln sin c x tg x dx + + = ) 4 2 ( ln cos π c a x a x a x dx x a + + - = - arcsin 2 2 2 2 2 2 2 , 0 > a c A x x A A x x dx A x + + + + + = + 2 2 2 ln 2 2 Dužina luka krive: dx x f l b a ′ + = 2 )) ( ( 1 , dt t y t x l t t t t ′ + ′ = 2 1 2 2 )) ( ( )) ( ( , ϕ ϕ ρ ϕ ρ β α d l ′ + = 2 2 )) ( ( ) ( . Zapremina obrtnih tela: = b a dx x f V ) ( 2 π , ′ ⋅ = 2 1 ) ( 2 t t t dt (t) x t y V π , = β α ϕ ϕ ϕ ρ π d V sin ) ( 3 2 3 . Površina omota a obrtnih tela: ′ + = b a dx x f x f P 2 )) ( ( 1 ) ( 2 π , dt t y t x t y P t t ′ + ′ = 2 1 2 2 )) ( ( )) ( ( ) ( 2 π , ϕ ϕ ϕ ρ ϕ ρ ϕ ρ π β α d P sin )) ( ( ) ( ) ( 2 2 2 ′ + = .
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Tablica osnonvih izvoda i integrala. Osnovni trigonometrijski identitetni. Korisno priliko rješavanja zadataka vezanih da ovu problematku
Transcript of Tablice Izvoda Integrala Trigonometrija
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Tablica izvoda:
Funkcija ( )xf Izvod (x)f
constc =
0
x
1
x 1x
xa aa x ln
xe xe
xalog ax ln
1
x ln x
1
xsin
xcos
xcos
xsin
tgx
x2cos
1
ctgx x
2sin1
xarcsin 21
1
x
xarccos 21
1
x
arctgx 21
1x+
arcctgx 21
1x+
Povrine ravnih figura:
=
b
a
dxxfP )( , =2
1
)(t
t
t dt(t)xtyP , =
dP )(21 2
.
Tablica integrala:
+= cxdx
cn
xdxxn
n ++
=
+
1
1
+= c x x
dx ln
+= cedxe xx
ca
adxax
x +=
ln
+= cxxdx cossin
+= cxxdx sincos
ctgxx
dx+=
2cos
cctgxx
dx+=
2sin
12211
ca
xarcctg
ac
a
xarctg
aax
dx+=+=
+
, 0a
c ax
ax
aax
dx+
+
=
ln21
22 , 0a
c axx ax
dx++=
2222
ln , 0a
122
arccosarcsin ca
xc
a
x
xa
dx+=+=
, 0>a
c x
tg x
dx+=
2ln
sin
c x
tg x
dx++=
)42
(lncos
pi
ca
xaxa
xdxxa ++=
arcsin22
22222
, 0>a
c Axx AAxxdx Ax +++++=+
222 ln22
Duina luka krive: dxxflb
a
+= 2))((1 , dttytxlt
t
tt
+=2
1
22 ))(())(( ,
dl += 22 ))(()( .
Zapremina obrtnih tela: =b
a
dxxfV )(2pi , =2
1
)(2t
t
t dt(t) xtyV pi , =
pi d V sin)(3
2 3.
Povrina omota a obrtnih tela:
+=b
a
dxxfxfP 2))((1)(2pi , dt tytxtyPt
t
+=2
1
22 ))(())(()(2pi , pi
d P sin))(()()(2 22
+= .
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Maklorenove formule:
)(!)1(...!2!11
12xR
n
x
x
xe n
nx +
++++=
, x
! )( e
n
xxR
n
n= , Rx
