NCERT Solutions class 12 Maths Exercise 7.10 (Ex 7.10) Chapter 7 Integrals

NCERT Solutions for Class 12 Maths Exercise 7.10 hapter 7 Integrals – FREE PDF Download

NCERT Solutions for integrals Class 12 exercises 7.10 are accessible in PDF format which is available at CoolGyan’s online learning portal. The solutions to this particular exercise from chapter 7 Integrals have been prepared by our experts who have years of experience in this field. Students can find, well-explained solutions to maths problems at CoolGyan’s online learning portal. All the solutions are provided in a way that will help you in understanding the concept effectively. You can download them in PDF format for free.

NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.10) Exercise 7.10



Evaluate the integrals in Exercises 1 to 8 using substitutions.
1.  
Ans. Let I = 
 ……….(i)
Putting 
  
 
To change the limits of integration from x to t
when x = 0, t = x2 +1 = 0 +1 = 1
when x =1, t = x2 +1 = 1 +1 = 2
  From eq. (i),





 Ans.

2. 
Ans. Let I =  ……….(i)
Putting 
 
 
To change the limits of integration from  to 
When 
When 
  From eq. (i),
I = 







=23(t32)10+211(t112)1047(t72)10=23(t32)01+211(t112)01−47(t72)01



 Ans.


3.   
Ans. Let I =  ……….(i)
Putting 
 
 
Limits of integration, when  
when 
 
  From eq. (i),
I = 



[Applying Product Rule]







 Ans.


4.   
Ans. Let I =  ……….(i)
Putting 
 
 
 
Limits of integration when  and when 
  From eq. (i),
I = 








 Ans.


5. 
Ans. Let I = 
 ……….(i)
Putting 
  
 
Limits of integration when  and when 
  From eq. (i), I = 



 Ans.


6. 
Ans. 









=117log(17+3173×17+1171)=117log⁡(17+317−3×17+117−1)






 Ans.


7. 
Ans. Let I = 

……….(i)
Putting 
  
 
Limits of integration when  and when 
  From eq. (i), I = 




 Ans.


8.   
Ans. Let I =  ……….(i)
Putting 
 
 
 
Limits of integration when  and when 
  From eq. (i),
I = 





=(ett)42=(ett)24


 Ans.


Choose the correct answer in Exercises 9 and 10.
9.  The value of the integral   is:
(A) 6
(B) 0
(C) 3
(D) 4
Ans. Let I = 



……….(i)
Putting 
 
 
Limits of integration when
 and when 
  From eq. (i),
I = 





Therefore, option (A) is correct.


10. If   then   is:
(A) 
(B) 
(C) 
(D)   
Ans.  

[Applying Product Rule]






Therefore, option (B) is correct.

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