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0, −1 <  < 0
1. () = {
, 0 <  < 1
Penyelesaian :
1
∫ () ()
= 
−1
0
2
2 + 1
1
∫ 0 . 0 () + ∫  . 0 () = 0
−1
0
2
2(0) + 1
1
0 + ∫  . 1 
= 0 . 2
0
1
∫  
= 0 . 2
0
1 2 1
 |
2
0
= 0 . 2
1
1
(1)2 − (0)2 = 0 .2
2
2
1
= 0 .2
2
0 =
1
4
1
∫ () ()
= 
−1
0
2
2 + 1
1
∫ 0 . 1 () + ∫  . 1 () = 1
−1
0
2
2(1) + 1
1
0 + ∫  .  
0
= 1 .
1
∫  2 
0
1 3 1
 |
3
0
= 1 .
= 1 .
2
3
2
3
2
3
1
1
2
(1)3 − (0)3 = 1 .
3
3
3
1
2
= 1 .
3
3
1 =
1
2
1
∫ () ()
= 
−1
0
2
2 + 1
1
∫ 0 . 2 () + ∫  . 2 () = 2
−1
0
1
1
0 + ∫  . ( (3 2 − 1)) 
2
0
1
3
1
∫ (  3 − ) 
2
0 2
3 4 1 2 1
 −  |
8
4
0
2
2(2) + 1
= 2 .
2
5
= 2 .
2
5
= 2 .
2
5
3
1
2
(1)4 − (0)2 = 2 .
8
4
5
3 1
2
−
= 2 .
8 4
5
2 =
() =
5
16
1
1
5
0 () + 1 () +
 () + … … …
4
2
16 2


∑ ∫  sin  . cos   = 0
=1 −


1
∑ ∫  ( (sin( + ) + sin( − )) ) 
2
−
=1



(sin( + 1) + sin( − 1)) 
− 2
∑∫
=1

∑
=1

∑
=1

∑
=1

∑
=1
 
∫ (sin( + 1) + sin( − 1)) 
2 −

1
1

cos ( + 1)  −
cos( − 1) )]
[(−
2
+1
−1
−

1
1
cos ( + 1)  +
cos( − 1) )
[(−
2
+1
−1
1
1
− (
cos ( + 1)(−) −
cos( − 1) − )]
+1
−1

[0 − 0]
2
=0

1
1

0 cos   = [ 0 sin ]
2
−
− 2
1
1
= [ 0 sin  − 0 sin(−) ]
2
2
=0+
=0+0
=0
∫

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