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# NCERT Solutions - Integrals, Exercise - 7.5 JEE Notes | EduRev

## JEE : NCERT Solutions - Integrals, Exercise - 7.5 JEE Notes | EduRev

``` Page 1

1 	 / 	 2 9
C B S E 	 C l a s s â€“ 1 0 	 M a t h e m a t i c s
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 5
I n t e g r a t e 	 t h e 	 ( r a t i o n a l ) 	 f u n c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 6 .
1 .
A n s . 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 	 o n 	 b o t h 	 s i d e s 	 A 	 + 	 B 	 = 	 1 	 . . . . . ( i i )
C o m p a r i n g 	 c o n s t a n t s 	 2 A 	 + 	 B 	 = 	 0 	 . . . . . ( i i i )
S o l v i n g 	 e q . 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 a n d 	 B 	 = 	 2
P u t t i n g 	 t h e s e 	 v a l u e s 	 o f 	 A 	 a n d 	 B 	 i n 	 e q . 	 ( i ) ,

=
Page 2

1 	 / 	 2 9
C B S E 	 C l a s s â€“ 1 0 	 M a t h e m a t i c s
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 5
I n t e g r a t e 	 t h e 	 ( r a t i o n a l ) 	 f u n c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 6 .
1 .
A n s . 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 	 o n 	 b o t h 	 s i d e s 	 A 	 + 	 B 	 = 	 1 	 . . . . . ( i i )
C o m p a r i n g 	 c o n s t a n t s 	 2 A 	 + 	 B 	 = 	 0 	 . . . . . ( i i i )
S o l v i n g 	 e q . 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 a n d 	 B 	 = 	 2
P u t t i n g 	 t h e s e 	 v a l u e s 	 o f 	 A 	 a n d 	 B 	 i n 	 e q . 	 ( i ) ,

=
2 	 / 	 2 9
=
2 .
A n s .
=
=
=
3 .
A n s .
= 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 A 	 + 	 B 	 + 	 C 	 = 	 0 	 . . . . . . . ( i i )
Page 3

1 	 / 	 2 9
C B S E 	 C l a s s â€“ 1 0 	 M a t h e m a t i c s
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 5
I n t e g r a t e 	 t h e 	 ( r a t i o n a l ) 	 f u n c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 6 .
1 .
A n s . 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 	 o n 	 b o t h 	 s i d e s 	 A 	 + 	 B 	 = 	 1 	 . . . . . ( i i )
C o m p a r i n g 	 c o n s t a n t s 	 2 A 	 + 	 B 	 = 	 0 	 . . . . . ( i i i )
S o l v i n g 	 e q . 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 a n d 	 B 	 = 	 2
P u t t i n g 	 t h e s e 	 v a l u e s 	 o f 	 A 	 a n d 	 B 	 i n 	 e q . 	 ( i ) ,

=
2 	 / 	 2 9
=
2 .
A n s .
=
=
=
3 .
A n s .
= 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 A 	 + 	 B 	 + 	 C 	 = 	 0 	 . . . . . . . ( i i )
3 	 / 	 2 9
C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 â€“ 5 A 	 â€“ 	 4 B 	 â€“ 	 3 C = 	 3
5 A 	 + 	 4 B 	 + 	 3 C 	 = 	 â€“ 3 	 . . . . . . . ( i i i )
C o m p a r i n g 	 c o n s t a n t s : 	 6 A 	 + 	 3 B 	 + 	 2 C 	 = 	 â€“ 1 	 . . . . . . . ( i v )
O n 	 s o l v i n g 	 e q . 	 ( i ) , 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 1 , 	 B 	 = 	 â€“ 5 , 	 C 	 = 	 4
P u t t i n g 	 t h e 	 v a l u e s 	 o f 	 A , 	 B 	 a n d 	 C 	 i n 	 e q . 	 ( i ) ,
=

=

=
4 .
A n s .
= 	 	 . . . . . . . ( i )

Page 4

1 	 / 	 2 9
C B S E 	 C l a s s â€“ 1 0 	 M a t h e m a t i c s
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 5
I n t e g r a t e 	 t h e 	 ( r a t i o n a l ) 	 f u n c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 6 .
1 .
A n s . 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 	 o n 	 b o t h 	 s i d e s 	 A 	 + 	 B 	 = 	 1 	 . . . . . ( i i )
C o m p a r i n g 	 c o n s t a n t s 	 2 A 	 + 	 B 	 = 	 0 	 . . . . . ( i i i )
S o l v i n g 	 e q . 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 a n d 	 B 	 = 	 2
P u t t i n g 	 t h e s e 	 v a l u e s 	 o f 	 A 	 a n d 	 B 	 i n 	 e q . 	 ( i ) ,

=
2 	 / 	 2 9
=
2 .
A n s .
=
=
=
3 .
A n s .
= 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 A 	 + 	 B 	 + 	 C 	 = 	 0 	 . . . . . . . ( i i )
3 	 / 	 2 9
C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 â€“ 5 A 	 â€“ 	 4 B 	 â€“ 	 3 C = 	 3
5 A 	 + 	 4 B 	 + 	 3 C 	 = 	 â€“ 3 	 . . . . . . . ( i i i )
C o m p a r i n g 	 c o n s t a n t s : 	 6 A 	 + 	 3 B 	 + 	 2 C 	 = 	 â€“ 1 	 . . . . . . . ( i v )
O n 	 s o l v i n g 	 e q . 	 ( i ) , 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 1 , 	 B 	 = 	 â€“ 5 , 	 C 	 = 	 4
P u t t i n g 	 t h e 	 v a l u e s 	 o f 	 A , 	 B 	 a n d 	 C 	 i n 	 e q . 	 ( i ) ,
=

=

=
4 .
A n s .
= 	 	 . . . . . . . ( i )

4 	 / 	 2 9

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 A 	 + 	 B 	 + 	 C 	 = 	 0 	 . . . . . . . ( i i )
C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 â€“ 5 A 	 â€“ 	 4 B 	 â€“ 	 3 C = 	 1
5 A 	 + 	 4 B 	 + 	 3 C 	 = 	 â€“ 1 	 . . . . . . . ( i i i )
C o m p a r i n g 	 c o n s t a n t s : 	 6 A 	 + 	 3 B 	 + 	 2 C 	 = 	 0 	 . . . . . . . ( i v )
O n 	 s o l v i n g 	 e q . 	 ( i ) , 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 B 	 = 	 â€“ 2 , 	 C 	 =
P u t t i n g 	 t h e 	 v a l u e s 	 o f 	 A , 	 B 	 a n d 	 C 	 i n 	 e q . 	 ( i ) ,
=

=

=
5 .
Page 5

1 	 / 	 2 9
C B S E 	 C l a s s â€“ 1 0 	 M a t h e m a t i c s
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 5
I n t e g r a t e 	 t h e 	 ( r a t i o n a l ) 	 f u n c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 6 .
1 .
A n s . 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 	 o n 	 b o t h 	 s i d e s 	 A 	 + 	 B 	 = 	 1 	 . . . . . ( i i )
C o m p a r i n g 	 c o n s t a n t s 	 2 A 	 + 	 B 	 = 	 0 	 . . . . . ( i i i )
S o l v i n g 	 e q . 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 a n d 	 B 	 = 	 2
P u t t i n g 	 t h e s e 	 v a l u e s 	 o f 	 A 	 a n d 	 B 	 i n 	 e q . 	 ( i ) ,

=
2 	 / 	 2 9
=
2 .
A n s .
=
=
=
3 .
A n s .
= 	 	 . . . . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 A 	 + 	 B 	 + 	 C 	 = 	 0 	 . . . . . . . ( i i )
3 	 / 	 2 9
C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 â€“ 5 A 	 â€“ 	 4 B 	 â€“ 	 3 C = 	 3
5 A 	 + 	 4 B 	 + 	 3 C 	 = 	 â€“ 3 	 . . . . . . . ( i i i )
C o m p a r i n g 	 c o n s t a n t s : 	 6 A 	 + 	 3 B 	 + 	 2 C 	 = 	 â€“ 1 	 . . . . . . . ( i v )
O n 	 s o l v i n g 	 e q . 	 ( i ) , 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 1 , 	 B 	 = 	 â€“ 5 , 	 C 	 = 	 4
P u t t i n g 	 t h e 	 v a l u e s 	 o f 	 A , 	 B 	 a n d 	 C 	 i n 	 e q . 	 ( i ) ,
=

=

=
4 .
A n s .
= 	 	 . . . . . . . ( i )

4 	 / 	 2 9

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 A 	 + 	 B 	 + 	 C 	 = 	 0 	 . . . . . . . ( i i )
C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 : 	 â€“ 5 A 	 â€“ 	 4 B 	 â€“ 	 3 C = 	 1
5 A 	 + 	 4 B 	 + 	 3 C 	 = 	 â€“ 1 	 . . . . . . . ( i i i )
C o m p a r i n g 	 c o n s t a n t s : 	 6 A 	 + 	 3 B 	 + 	 2 C 	 = 	 0 	 . . . . . . . ( i v )
O n 	 s o l v i n g 	 e q . 	 ( i ) , 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 B 	 = 	 â€“ 2 , 	 C 	 =
P u t t i n g 	 t h e 	 v a l u e s 	 o f 	 A , 	 B 	 a n d 	 C 	 i n 	 e q . 	 ( i ) ,
=

=

=
5 .
5 	 / 	 2 9
A n s .
=
=
=
= 	 	 . . . . ( i )

C o m p a r i n g 	 c o e f f i c i e n t s 	 o f 	 	 o n 	 b o t h 	 s i d e s 	 A 	 + 	 B 	 = 	 2 	 . . . . . . . ( i i )
C o m p a r i n g 	 c o n s t a n t s 	 2 A 	 + 	 B 	 = 	 0 	 . . . . . ( i i i )
S o l v i n g 	 e q . 	 ( i i ) 	 a n d 	 ( i i i ) , 	 w e 	 g e t 	 A 	 = 	 	 a n d 	 B 	 = 	 4
P u t t i n g 	 t h e s e 	 v a l u e s 	 o f 	 A 	 a n d 	 B 	 i n 	 e q . 	 ( i ) ,

```
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## Mathematics (Maths) Class 12

209 videos|222 docs|124 tests

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