NCERT Solutions - Integrals, Exercise - 7.3 JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions - Integrals, Exercise - 7.3 JEE Notes | EduRev

 Page 1


1 	 / 	 2 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 . 3
F i n d 	 t h e 	 i n t e g r a l s 	 o f 	 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 . 	
= 	
U s i n g 	
= 	 	
= 	 	 	 	 	 	
U s i n g
= 	 	 A n s .
2 . 	
A n s . 	 	 	 = 	 	
= 	 	 	 	 	 	 	 	 U s i n g 	 2 s i n B 	 c o s A = s i n ( A + B ) - s i n ( A - B )
Page 2


1 	 / 	 2 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 . 3
F i n d 	 t h e 	 i n t e g r a l s 	 o f 	 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 . 	
= 	
U s i n g 	
= 	 	
= 	 	 	 	 	 	
U s i n g
= 	 	 A n s .
2 . 	
A n s . 	 	 	 = 	 	
= 	 	 	 	 	 	 	 	 U s i n g 	 2 s i n B 	 c o s A = s i n ( A + B ) - s i n ( A - B )
2 	 / 	 2 1
= 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	
= 	 	
= 	 	
= 	 	 A n s .
3 . 	 	
A n s . 	 	
= 	
= 	 	 	 	 	 	
	 U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
= 	 	
= 	 	 	 	 	 	 	 	
= 	 	 	 	
U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
a n d 	 	 	 	 	 	 	 	
= 	 	
Page 3


1 	 / 	 2 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 . 3
F i n d 	 t h e 	 i n t e g r a l s 	 o f 	 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 . 	
= 	
U s i n g 	
= 	 	
= 	 	 	 	 	 	
U s i n g
= 	 	 A n s .
2 . 	
A n s . 	 	 	 = 	 	
= 	 	 	 	 	 	 	 	 U s i n g 	 2 s i n B 	 c o s A = s i n ( A + B ) - s i n ( A - B )
2 	 / 	 2 1
= 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	
= 	 	
= 	 	
= 	 	 A n s .
3 . 	 	
A n s . 	 	
= 	
= 	 	 	 	 	 	
	 U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
= 	 	
= 	 	 	 	 	 	 	 	
= 	 	 	 	
U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
a n d 	 	 	 	 	 	 	 	
= 	 	
3 	 / 	 2 1
= 	 	 	 	 	 	 	 A n s .
4 . 	
A n s . 	 	
= 	 	
	
= 	 	
= 	 	
= 	 	
= 	
A n o t h e r 	 M e t h o d 	 	 	
	 	 	 	 	
U s i n g 	
	 	 	 	 l e t 	 	
	 	 t h e r e f o r e 	 	
Page 4


1 	 / 	 2 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 . 3
F i n d 	 t h e 	 i n t e g r a l s 	 o f 	 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 . 	
= 	
U s i n g 	
= 	 	
= 	 	 	 	 	 	
U s i n g
= 	 	 A n s .
2 . 	
A n s . 	 	 	 = 	 	
= 	 	 	 	 	 	 	 	 U s i n g 	 2 s i n B 	 c o s A = s i n ( A + B ) - s i n ( A - B )
2 	 / 	 2 1
= 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	
= 	 	
= 	 	
= 	 	 A n s .
3 . 	 	
A n s . 	 	
= 	
= 	 	 	 	 	 	
	 U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
= 	 	
= 	 	 	 	 	 	 	 	
= 	 	 	 	
U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
a n d 	 	 	 	 	 	 	 	
= 	 	
3 	 / 	 2 1
= 	 	 	 	 	 	 	 A n s .
4 . 	
A n s . 	 	
= 	 	
	
= 	 	
= 	 	
= 	 	
= 	
A n o t h e r 	 M e t h o d 	 	 	
	 	 	 	 	
U s i n g 	
	 	 	 	 l e t 	 	
	 	 t h e r e f o r e 	 	
4 	 / 	 2 1
	 	 	 	 t h u s 	
	 	 	 	 A n s
5 . 	
A n s . 	 	
= 	 	
= 	
= 	
= 	 	
= 	 	
= 	 	
= 	 	
= 	
Page 5


1 	 / 	 2 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 . 3
F i n d 	 t h e 	 i n t e g r a l s 	 o f 	 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 . 	
= 	
U s i n g 	
= 	 	
= 	 	 	 	 	 	
U s i n g
= 	 	 A n s .
2 . 	
A n s . 	 	 	 = 	 	
= 	 	 	 	 	 	 	 	 U s i n g 	 2 s i n B 	 c o s A = s i n ( A + B ) - s i n ( A - B )
2 	 / 	 2 1
= 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	
= 	 	
= 	 	
= 	 	 A n s .
3 . 	 	
A n s . 	 	
= 	
= 	 	 	 	 	 	
	 U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
= 	 	
= 	 	 	 	 	 	 	 	
= 	 	 	 	
U s i n g 	 2 c o s A 	 c o s B = c o s ( A + B ) + c o s ( A - B )
a n d 	 	 	 	 	 	 	 	
= 	 	
3 	 / 	 2 1
= 	 	 	 	 	 	 	 A n s .
4 . 	
A n s . 	 	
= 	 	
	
= 	 	
= 	 	
= 	 	
= 	
A n o t h e r 	 M e t h o d 	 	 	
	 	 	 	 	
U s i n g 	
	 	 	 	 l e t 	 	
	 	 t h e r e f o r e 	 	
4 	 / 	 2 1
	 	 	 	 t h u s 	
	 	 	 	 A n s
5 . 	
A n s . 	 	
= 	 	
= 	
= 	
= 	 	
= 	 	
= 	 	
= 	 	
= 	
5 	 / 	 2 1
A n o t h e r 	 m e t h o d 	 	 	 l e t 	 	 	 I = 	 	 	 	
l e t 	 c o s x = t
- s i n x 	 d x = d t
s i n x 	 	 d x 	 = 	 - d t
	 	 a n s .
	
6 . 	 	
A n s . 	 	
= 	 	
= 	 	 	 	 	 	 	 	 	 	 U s i n g 	 2 s i n 	 A 	 s i n 	 B = c o s 	 ( A - B ) 	 - 	 c o s 	 ( 	 A + B )
	 	
= 	 	 	
u s i n g 	 2 c o s A 	 s i n B = s i n ( A + B ) - s i n ( A - B )
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