Page 1
1 / 2 9
C B S E C l a s s – 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 – 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 – 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 : – 5 A – 4 B – 3 C = 3
5 A + 4 B + 3 C = – 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 = – 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 = – 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
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C B S E C l a s s – 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 : – 5 A – 4 B – 3 C = 3
5 A + 4 B + 3 C = – 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 = – 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 = – 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 : – 5 A – 4 B – 3 C = 1
5 A + 4 B + 3 C = – 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 = – 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 – 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 : – 5 A – 4 B – 3 C = 3
5 A + 4 B + 3 C = – 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 = – 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 = – 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 : – 5 A – 4 B – 3 C = 1
5 A + 4 B + 3 C = – 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 = – 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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