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NCERT Solutions Class 12 Maths Chapter 7 - Integrals

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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 	 	
	 	
	 	
	 	
= 	
= 	 	
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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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FAQs on NCERT Solutions Class 12 Maths Chapter 7 - Integrals

1. What are NCERT Solutions for Exercise- 7.8: Integrals?
Ans. NCERT Solutions for Exercise- 7.8: Integrals are the detailed explanations and solutions provided for the questions given in the exercise 7.8 of the NCERT textbook. These solutions help students understand the concepts of integrals and solve the problems effectively.
2. How can NCERT Solutions for Exercise- 7.8: Integrals be helpful for exam preparation?
Ans. NCERT Solutions for Exercise- 7.8: Integrals serve as a valuable resource for exam preparation. By referring to these solutions, students can get a clear understanding of the concepts and techniques related to integrals. They can also learn the step-by-step approach to solve the problems, which can be beneficial during exams.
3. Are the NCERT Solutions for Exercise- 7.8: Integrals available in the same language as the article title?
Ans. Yes, the NCERT Solutions for Exercise- 7.8: Integrals are available in the same language as the article title. These solutions are designed to cater to students who are studying in the language specified in the article title, ensuring that they can easily understand and comprehend the concepts.
4. How can I search for frequently asked questions related to integrals on Google?
Ans. To search for frequently asked questions related to integrals on Google, you can use specific keywords such as "integral FAQs," "common questions about integrals," or "integral problems and solutions." By using these keywords, you are more likely to find relevant and helpful FAQs about integrals.
5. Can I find additional practice questions related to integrals along with the NCERT Solutions for Exercise- 7.8?
Ans. Yes, along with the NCERT Solutions for Exercise- 7.8: Integrals, you can find additional practice questions related to integrals. These practice questions are designed to enhance your understanding and provide you with more opportunities to practice solving problems. They can be extremely helpful in strengthening your knowledge and skills in integrals.
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