2nd tri calculus flashcards

114
sin d u dx

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Transcript of 2nd tri calculus flashcards

Page 1: 2nd tri calculus flashcards

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