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