NCERT Solutions - Integrals, Exercise - 7.1 JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions - Integrals, Exercise - 7.1 JEE Notes | EduRev

 Page 1


1 	 / 	 1 3
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 . 1
F i n d 	 a n 	 a n t i d e r i v a t i v e 	 ( o r 	 i n t e g r a l ) 	 o f 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 b y 	 t h e 	 m e t h o d 	 o f
i n s p e c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 5 .
1 . 	 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
2 . 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
Page 2


1 	 / 	 1 3
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 . 1
F i n d 	 a n 	 a n t i d e r i v a t i v e 	 ( o r 	 i n t e g r a l ) 	 o f 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 b y 	 t h e 	 m e t h o d 	 o f
i n s p e c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 5 .
1 . 	 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
2 . 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
3 . 	 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
4 . 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
5 . 	 	
A n s . 	
Page 3


1 	 / 	 1 3
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 . 1
F i n d 	 a n 	 a n t i d e r i v a t i v e 	 ( o r 	 i n t e g r a l ) 	 o f 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 b y 	 t h e 	 m e t h o d 	 o f
i n s p e c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 5 .
1 . 	 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
2 . 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
3 . 	 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
4 . 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
5 . 	 	
A n s . 	
	 	 … . . ( i )
A g a i n 	 	
	 	
	 	 [ M u l t i p l y i n g 	 b o t h 	 s i d e s 	 b y 	 ] 	 … … … . ( i i )
A d d i n g 	 e q . 	 ( i ) 	 a n d 	 ( i i ) , 	 w e 	 g e t
	 	
	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 i n t e g r a l s 	 i n 	 E x e r c i s e s 	 6 	 t o 	 1 1 .
6 . 	 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	 	
Page 4


1 	 / 	 1 3
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 . 1
F i n d 	 a n 	 a n t i d e r i v a t i v e 	 ( o r 	 i n t e g r a l ) 	 o f 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 b y 	 t h e 	 m e t h o d 	 o f
i n s p e c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 5 .
1 . 	 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
2 . 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
3 . 	 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
4 . 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
5 . 	 	
A n s . 	
	 	 … . . ( i )
A g a i n 	 	
	 	
	 	 [ M u l t i p l y i n g 	 b o t h 	 s i d e s 	 b y 	 ] 	 … … … . ( i i )
A d d i n g 	 e q . 	 ( i ) 	 a n d 	 ( i i ) , 	 w e 	 g e t
	 	
	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 i n t e g r a l s 	 i n 	 E x e r c i s e s 	 6 	 t o 	 1 1 .
6 . 	 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	 	
7 . 	
A n s . 	 	 = 	 	 = 	 	 = 	 	
	 	
8 . 	 	
A n s . 	 	
= 	 	
= 	
= 	 	 w h e r e 	 	 i s 	 t h e 	 c o n s t a n t 	 o f 	 i n t e g r a t i o n .
9 . 	 	
A n s . 	 	
= 	 	
= 	
= 	 	
Page 5


1 	 / 	 1 3
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 . 1
F i n d 	 a n 	 a n t i d e r i v a t i v e 	 ( o r 	 i n t e g r a l ) 	 o f 	 t h e 	 f o l l o w i n g 	 f u n c t i o n s 	 b y 	 t h e 	 m e t h o d 	 o f
i n s p e c t i o n 	 i n 	 E x e r c i s e s 	 1 	 t o 	 5 .
1 . 	 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
2 . 	
A n s . 	
	
	 	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
3 . 	 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
4 . 	
A n s . 	 	 	
	
	 	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
5 . 	 	
A n s . 	
	 	 … . . ( i )
A g a i n 	 	
	 	
	 	 [ M u l t i p l y i n g 	 b o t h 	 s i d e s 	 b y 	 ] 	 … … … . ( i i )
A d d i n g 	 e q . 	 ( i ) 	 a n d 	 ( i i ) , 	 w e 	 g e t
	 	
	
	 A n 	 a n t i - d e r i v a t i v e 	 o f 	 	 i s 	 	
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 i n t e g r a l s 	 i n 	 E x e r c i s e s 	 6 	 t o 	 1 1 .
6 . 	 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	 	
7 . 	
A n s . 	 	 = 	 	 = 	 	 = 	 	
	 	
8 . 	 	
A n s . 	 	
= 	 	
= 	
= 	 	 w h e r e 	 	 i s 	 t h e 	 c o n s t a n t 	 o f 	 i n t e g r a t i o n .
9 . 	 	
A n s . 	 	
= 	 	
= 	
= 	 	
1 0 . 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
= 	 	
1 1 . 	 	
A n s . 	 	
= 	 	
= 	 	
= 	 	
= 	 	
= 	 	
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