Final EngHin NNNN
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1
x
xe f (x)
e=
(a)
1( a)
{ (1 )} and f
f I x g x x dx=
(a)
2( a)
{ (1 )} f
f I g x x dx=
2
1
I I
12
1
x
xe f (x)
e=
(a)
1( a)
{ (1 )} f
f I x g x x dx=
(a)
2( a)
{ (1 )} f
f I g x x dx=
2
1
I
I
12
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1374
2454
1474
454
(1 )(1 )
z zz z
22 sin2
22 cos2
1 cos2
1 sin2
1 1 1
p q rx x
2 21 (p q )2
2 21 (p q )2
2 21 (p q )2
1374
2454
1474
454
(1 )(1 )z zz z
22 sin2
22 cos2
1 cos2
1 sin2
1 1 1
p q rx x
2 21 (p q )2
2 21 (p q )2
2 21 (p q )2
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10 1k
k S
=
2n k S
2n k S
2 1n k S
2 1n k S
,a , b c
d
( ) ( ) 1 1 1 6 3 3
a b c d i j k
a
b
c
2 23
i j k
2 23
i j k
2 23
i j k
23
i j k
10 1k
k S
=
2n k S
2n k S
2 1n k S
2 1n k S
,a , b c
d
( ) ( ) 1 1 1 6 3 3
a b c d i j k
a
b
c
2 23
i j k
2 23
i j k
2 23
i j k
23
i j k
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3 3 3 32 31
1 1 1 1x x x p
=
2 2 2 22 31x x x p=
1 2 3
1 1 1 1x x x p=
22 2 22 31
1 1 1 1x x x p
=
3 3 3 32 31
1 1 1 1x x x p
=
2 2 2 22 31x x x p=
1 2 3
1 1 1 1x x x p=
22 2 22 31
1 1 1 1x x x p
=
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11 01
a bc ab c
=
3 32
94
54
11 01
a bc ab c
=
3 32
94
54
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4 3 ,2 2
16 9 ,5 5
143 1 ,3 4
8 77 ,9 3
2 4 = =
1 1 3 yx z
2 = =
1 2 4 yx z
4 3 ,2 2
16 9 ,5 5
143 1 ,3 4
8 77 ,9 3
2 4 = =1 1 3
yx z
2 = =
1 2 4 yx z
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10 ,e
1 1,
e
2
5 2 5
1 5 f (x)sin x dx Ccos x sin x cos x
=
10 ,e
1 1,
e
2
5 2 5
1 5 f (x)sin x dx Ccos x sin x cos x
=
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3 < 2
2
if xx f (x)a bx if x
=
1 1 = and =4 16
a b
3 1 = and =4 16
a b
3 1 = and =4 16
a b
1 1 = and =4 16
a b
2
1 > 2
2
xx f (x)a bx x
=
1 1 = =4 16
a b
3 1 = =4 16
a b
3 1 = =4 16
a b
1 1 = =4 16
a b
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25
14
23
12
13
2
5 1
42
31
21
3
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