2nd tri calculus flashcards
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TRANSCRIPT
sind udx
(cos ) 'u u
cosd udx
(sin ) 'u u
tand udx
2(sec ) 'u u
cotd udx
2(csc ) 'u u
cscd udx
(csc cot ) 'u u u
nd udx
1( ) 'nn u u
d cdx
0
d udx v
2
' 'vu uvv
d u vdx
' 'u v v u
d udx
( '), 0u u uu
ud edx
'ue u
lnd udx
'uu
logad udx
'
lnua u
ud adx
ln 'ua a u
arcsind udx
2
'
1
u
u
arccosd udx
2
'
1
u
u
arctand udx
2
'1uu
arccotd udx
2
'1uu
arcsecd udx
2
'
1
u
u u
arccscd udx
2
'
1
u
u u
d xdx
1
d u vdx
' 'u v
d cudx
'cu
( )kf u du
( )k f u du
[ ( ) ( )]f u g u du
( ) ( ) f u du g u du
du
u C
nu du
1
1
nu Cn
duu
ln u C
ue du
ue C
sin u du
cosu C
cos u du
sinu C
2sec u du
tanu C
2csc u du
cotu C
csc cot u u du
cscu C
sec tan u u du
secu C
cot u du
ln sinu C
tan u du
ln cosu C
csc u du
ln csc cotu u C
sec u du
ln sec tanu u C
ua du
1ln
ua Ca
2 2 du
a u
arcsin u Ca
2 2 du
u u a
1 arcsecu
Ca a
2 2 duu a
1 arctan u Ca a
1
n
i
c
cn
1
n
i
i
12
n n
2
1
n
i
i
1 2 16
n n n
3
1
n
i
i
22 14
n n
Fundamental Theorem of Calculus
( )b
a
f x dx
( ) ( ) ( )b
aF x F b F a
2nd Fundamental Theorem of Calculus
( )x
a
d f t dtdx
( )f x
Mean Value TheoremThere exists x=c such that
( )b
a
f x dx
( ) ( )f c b a
1 ( )b
a
f x dxb a
Average Value (Average Height of
area)
Definition of the Natural Logarithmic Function
1
1 , 0x
dt xt
ln x
Definition of exponential function base a
xa =
(ln )a xe
Definition of logarithmic function base a
alog x
1 lnln
xa
1lim 1x
x x
e
rtA Pe
Account with continuous interest
1ntrA P
n
Account with interest compounded “n” times
a year