Page 57 - MODUL Kalkulus Lanjut

Contoh

2 2 cos 4 −r 2
1)    rdzdrd 
0 0 0
Jawab


2 2 cos  4 −r 2 2
   rdzdrd  =  ( ) 4 0 −r dr d 
rz
0 0 0


2 2 cos
  (4r − r 3 )dr d 
=
0 0


2  1  2 cos
=  2r 2 − r 4  d 
0  4  0

2

=
2
4
4
( cos  − cos  d
4
) 
0

2
2
4
) 
= 4  (cos  − cos  d
0

2
4
2
= 4  (cos  − cos  ) d
0
 
3
 sin cos 1  2  sin cos  3  sin cos 1   2
= 4 −   − 4  −  −    
 2 2 0   4 4  2 2 0  
1  3 
= . 8 . − . 4 .
2 2 8 2
5
=
4


2 2 sin  4
2.    rdzdrd 

0 0 r 2

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