NCERT Solutions - Integrals, Exercise - 7.8 JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions - Integrals, Exercise - 7.8 JEE Notes | EduRev

 Page 1


1 	 / 	 6
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 . 8
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 d e f i n i t e 	 i n t e g r a l s 	 a s 	 l i m i t 	 o f 	 s u m s :
1 . 	 	 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	 	
H e r e , 	 	 a n d 	 	
	 	
	 	
	 	
= 	
= 	 	
Page 2


1 	 / 	 6
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 . 8
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 d e f i n i t e 	 i n t e g r a l s 	 a s 	 l i m i t 	 o f 	 s u m s :
1 . 	 	 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	 	
H e r e , 	 	 a n d 	 	
	 	
	 	
	 	
= 	
= 	 	
2 	 / 	 6
= 	
= 	
= 	 	
= 	
= 	 	
2 . 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
w h e r e 	 	
H e r e , 	 	 a n d 	 	
Page 3


1 	 / 	 6
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 . 8
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 d e f i n i t e 	 i n t e g r a l s 	 a s 	 l i m i t 	 o f 	 s u m s :
1 . 	 	 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	 	
H e r e , 	 	 a n d 	 	
	 	
	 	
	 	
= 	
= 	 	
2 	 / 	 6
= 	
= 	
= 	 	
= 	
= 	 	
2 . 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
w h e r e 	 	
H e r e , 	 	 a n d 	 	
3 	 / 	 6
= 	
= 	
= 	 	 = 	 	
3 . 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	
H e r e , 	 	 a n d 	 	
= 	
= 	 	
Page 4


1 	 / 	 6
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 . 8
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 d e f i n i t e 	 i n t e g r a l s 	 a s 	 l i m i t 	 o f 	 s u m s :
1 . 	 	 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	 	
H e r e , 	 	 a n d 	 	
	 	
	 	
	 	
= 	
= 	 	
2 	 / 	 6
= 	
= 	
= 	 	
= 	
= 	 	
2 . 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
w h e r e 	 	
H e r e , 	 	 a n d 	 	
3 	 / 	 6
= 	
= 	
= 	 	 = 	 	
3 . 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	
H e r e , 	 	 a n d 	 	
= 	
= 	 	
4 	 / 	 6
= 	 	 = 	
4 . 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
w h e r e 	 	
H e r e , 	 	 a n d 	 	
= 	
= 	
= 	 	 = 	 	
5 . 	 	 	 	
Page 5


1 	 / 	 6
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 . 8
E v a l u a t e 	 t h e 	 f o l l o w i n g 	 d e f i n i t e 	 i n t e g r a l s 	 a s 	 l i m i t 	 o f 	 s u m s :
1 . 	 	 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	 	
H e r e , 	 	 a n d 	 	
	 	
	 	
	 	
= 	
= 	 	
2 	 / 	 6
= 	
= 	
= 	 	
= 	
= 	 	
2 . 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
w h e r e 	 	
H e r e , 	 	 a n d 	 	
3 	 / 	 6
= 	
= 	
= 	 	 = 	 	
3 . 	 	
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	
H e r e , 	 	 a n d 	 	
= 	
= 	 	
4 	 / 	 6
= 	 	 = 	
4 . 	 	 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
w h e r e 	 	
H e r e , 	 	 a n d 	 	
= 	
= 	
= 	 	 = 	 	
5 . 	 	 	 	
5 	 / 	 6
A n s . 	 W e 	 k n o w 	 t h a t
w h e r e 	 	
H e r e , 	 	 a n d 	 	
[ 	 T h e 	 s e r i e s 	 w i t h i n 	 b r a c k e t s 	 i s 	 a 	 G . P . 	 a n d 	 ]
S o , 	 W e 	 g e t 	
	
= 	
= 	
6 . 	 	
A n s . 	 W e 	 k n o w 	 t h a t 	
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