DIFERENSIAL PARSIAL

DIFERENSIAL PARSIAL

1.      Tentukan f_x, f_y, f_xy, f_xyx

a.       f( x,y) = 3x² . sin y²

jawab :

f( x,y) =

misal :     u   = 3x²

               u’  = 6x

               v   = sin y²

               v   = 0

f_x(x,y)     =   u’ . v + u . v’

               =   6x . sin y² + 3x² . 0

               =   6x sin y²

F_y(x,y)    =  

Misal :    u   = 3x²

               u’ = 0

               v   = sin y²

               v’  = 2 y cos y²

fy(x,y)    =   u’ . v + u . v’

               =   0 . sin y² + 3 x² . 2y cos y²

               =   6 x²y . cos y²

F_xy(x,y)   =  

Misal :    u   = 6x

               u’ = 0

               v   = sin y²

               v’  = 2 y cos y²

fy(x,y)    =   u’ . v + u . v’

               =   0 . sin y² + 3 x² . 2y cos y²

               =   6 x²y . cos y²

F_xyx(x,y)  =  

Misal :    u   = 12xy

               u’ = 12

               v   = cos y²

               v’  = -2 y sin y²

fy(x,y)    =   u’ . v + u . v’

               =   12y . cos y² + 12 xy . (- 2y sin y²)

               =   12y cos y² – cos y x y² . sin y²

b.      f( x,y) = x² .

Jawab :

f( x,y) =

misal :     u   = x²

               u’  = 2x

               v   =

               v   =

f_x(x,y)     =   u’ . v + u . v’

               =   2x . +  x² .

               =   2x . +

2.      Jika f ( x,y)  = x² - 3xy  + 2y – 3y + 5

a.       Hitung

f_x (2,3)    =   2x – 3y + 2

               =   2 (2)  – 3 (3)  + 2

               =   -3

b.      Hitung

f_y (2,3)    =   -3x – 3

               =   -3 ( 9 ) – 3

               =   -9

3.       

Tentukan

a.       f_t( t = x ) =

misal :     u   =  t x

               u’  = -2 x sin 2 t x

               v   = t2 + x2

               v   = 2t

f_x(x,y)     =

            = 

            = 

            = 

b.      f_x( t = x ) =

misal :     u   =  t x

               u’  = -2 x sin 2 t x

               v   = t2 + x2

               v   = 2x

f_x(x,y)     =

            = 

            = 

            = 

30 maret 2010

INTEGRAL PANGKAT

a.         =  

                     =  

                     =    

                     =  

                     =   y

                     =   ( y2 – y1 )

                     =   (4 – 2)

                     =   2

b.          =  

                     =  

                     =  

                     =  

                     =  

                     =  

                     =  

                     =  

                     =

c.       .   =  

 = x2              

            v       = 

                     =  

                     =  

                     =  

                     = 

                     =  

                     =  

                     =  

                     =  

                     =  

                     =  

                         

INTEGTAL GARIS

1.      Hitung  melalui persamaan garis dari (0,1) ke (1,2)

Jawab :

                      =  

                         =  

               y - 1            =     x

                    y            =     x + 1

 

ó  

ó

ó

ó   +  

ó(   + { (

ó(  -  - 1 ) + (   + 2 – 2 ) – (  +  - 1 )

ó(  +  - 1 ) +    -  + 1 )

ó   - 1

ó  

2.      Hitung   disepanjang x = t dan y = t² + 1

 = 1                = 2t

                dy = 2t dt

x = t                               y = t² + 1

x₁ = 0 ¦t₁ = 0               y₁= 1 ¦t₁ = 0

x₂ = 1 ¦t₂ = 1               y₂= 2 ¦t₂ = 1

ó  

ó

ó

ó (

ó -1

ó

SISTEM KOORDINAT