NCERT Solutions Exercise- 7.4: Integrals - Notes | Study Mathematics (Maths) Class 12 - JEE

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 Page 1


1 	 / 	 3 1
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 . 4
I n t e g r a t e 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 9 .
1 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
I 	 = 	 	
= 	 	 	 	 	 	 	 	 	 	 	 	 u s i n g 	
= 	 	 	 A n s .
2 . 	 	
Page 2


1 	 / 	 3 1
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 . 4
I n t e g r a t e 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 9 .
1 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
I 	 = 	 	
= 	 	 	 	 	 	 	 	 	 	 	 	 u s i n g 	
= 	 	 	 A n s .
2 . 	 	
2 	 / 	 3 1
A n s . 	
= 	
= 	
	
= 	
3 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
Page 3


1 	 / 	 3 1
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 . 4
I n t e g r a t e 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 9 .
1 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
I 	 = 	 	
= 	 	 	 	 	 	 	 	 	 	 	 	 u s i n g 	
= 	 	 	 A n s .
2 . 	 	
2 	 / 	 3 1
A n s . 	
= 	
= 	
	
= 	
3 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
3 	 / 	 3 1
4 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
5 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
Page 4


1 	 / 	 3 1
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 . 4
I n t e g r a t e 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 9 .
1 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
I 	 = 	 	
= 	 	 	 	 	 	 	 	 	 	 	 	 u s i n g 	
= 	 	 	 A n s .
2 . 	 	
2 	 / 	 3 1
A n s . 	
= 	
= 	
	
= 	
3 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
3 	 / 	 3 1
4 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
5 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
4 	 / 	 3 1
I 	 = 	 	
= 	 	
= 	 	
= 	 	
= 	 	 A n s .
6 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	
= 	 	 … … … . ( i )
P u t t i n g 	
	
	 	
F r o m 	 e q . 	 ( i ) ,
Page 5


1 	 / 	 3 1
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 . 4
I n t e g r a t e 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 9 .
1 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
I 	 = 	 	
= 	 	 	 	 	 	 	 	 	 	 	 	 u s i n g 	
= 	 	 	 A n s .
2 . 	 	
2 	 / 	 3 1
A n s . 	
= 	
= 	
	
= 	
3 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
3 	 / 	 3 1
4 . 	 	
A n s . 	 	
= 	 	
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= 	 	
5 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	 	 … … … . ( i )
P u t t i n g 	
	 	
	 	
	 	 F r o m 	 e q . 	 ( i ) ,
4 	 / 	 3 1
I 	 = 	 	
= 	 	
= 	 	
= 	 	
= 	 	 A n s .
6 . 	 	
A n s . 	 L e t 	 I 	 = 	
= 	
= 	 	 … … … . ( i )
P u t t i n g 	
	
	 	
F r o m 	 e q . 	 ( i ) ,
5 	 / 	 3 1
I 	 = 	
= 	 	
= 	
	
	 = 	 	
7 . 	 	
A n s . 	 L e t 	 I 	 = 	 	
= 	 	
= 	 	
L e t 	 I
1
	 = 	 	
P u t t i n g

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