NCERT Solutions class 12 Maths Exercise 7.2 (Ex 7.2) Chapter 7 Integrals

NCERT Solutions for Class 12 Maths Exercise 7.2 hapter 7 Integrals – FREE PDF Download

NCERT Solutions for integrals Class 12 exercises 7.2 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 7.2) Exercise 7.2



Integrate the functions in Exercise 1 to 8.
1. 
Ans. Putting   

 



 

2. 

 

Ans. Putting   
 
 
 



3. 

 

Ans. Putting   
 
 
 



4. 

 

Ans. Putting   
 
 
 



 = 

5. 

 

Ans.   

12sin2(ax+b)dx12∫sin⁡2(ax+b)dx

12[cos(2ax+2b)2a]+c12[−cos⁡(2ax+2b)2a]+c                     [  becauseSin(ax+b)dx=1aCos(ax+b)∫Sin(ax+b)dx=−1aCos(ax+b)]

6. 

 

Ans.   

Using  (ax+b)ndx=(ax+b)n+1a(n+1)+c∫(ax+b)ndx=(ax+b)n+1a(n+1)+c  We have


7. 

 

Ans.   




Using  (ax+b)ndx=(ax+b)n+1a(n+1)+c∫(ax+b)ndx=(ax+b)n+1a(n+1)+c
 


8. 

 

Ans. Let I =   
 ……….(i)
Putting 

 
From eq. (i),
I = 




Integrate the functions in Exercise 9 to 17.

 
9. 

Ans. Let I =   

 …..(i)
Putting 
 
 
 From eq. (i), I = 




10. 

 

Ans. Let I =  ……….(i) 
Putting 
 
 
 
From eq. (i),
I = 




11. 

 

Ans.   




          Using  (ax+b)ndx=(ax+b)n+1a(n+1)+c∫(ax+b)ndx=(ax+b)n+1a(n+1)+c

2x+4−−−−√(x+434)+c2x+4(x+43−4)+c
2x+4−−−−√(x+4123)+c2x+4(x+4−123)+c

12. 

 

Ans. Let I =   

 ……….(i)
Putting 

 
 
From eq. (i), I = 






13. 

 

Ans. Let I =   
……….(i)
Putting 

 
From eq. (i), I = 



14. 

 

Ans. Let I =   
……….(i)
Putting 
 
 
From eq. (i), I =   = 


15. 

 

Ans. Let I =   
……….(i)
Putting 
 
 
From eq. (i), I =   = 


16. 

 

Ans.   
         Usingeax+bdx=eax+ba+c∫eax+bdx=eax+ba+c

17. 

 

Ans. Let I =   
……….(i
Putting 
 
 
From eq. (i), I =   = 
using   eax+bdx=eax+ba+c∫eax+bdx=eax+ba+c
We have    =12(et1)+c=12(e−t−1)+c


Integrate the functions in Exercise 18 to 26.

 
18. 

Ans. Let I =   ……….(i) 
Putting 

 
From eq. (i), I = 


19. 

 

Ans. Let I =   
 [Multiplying each term by  ]
Putting 
 
 
From eq. (i), I =   = 



20. 

 

Ans. Let I =   
……….(i)
Putting 
 
 
 
From eq. (i), I = 



21. 

 

Ans.   


Using  sec2(ax+b)dx=tan(ax+b)a+c∫sec2(ax+b)dx=tan⁡(ax+b)a+c
=tan(2x3)2x+c=tan⁡(2x−3)2−x+c

22. 

 

Ans.   
Using   sec2(ax+b)dx=tan(ax+b)a+c∫sec2(ax+b)dx=tan⁡(ax+b)a+c

23. 

 

Ans. Let I =  ……….(i) 
Putting 
 
 
From eq. (i), I = 


24. 

 

Ans. Let I =   

……….(i)
Putting 
 
 
From eq. (i), I =   = 

25. 

 

Ans. Let I =   

……….(i)
Putting 

 
From eq. (i),  I =   = 



26. 

 

Ans. Let I =  ……….(i) 
Putting 
 
 
 
From eq. (i),  I = 


=

Integrate the functions in Exercise 27 to 37.

 
27. 

Ans. Let I =   
 ……….(i)
Putting 
 
 
From eq. (i),  I = 




28. 

 

Ans. Let I =  ……….(i) 
Putting 
 
 
From eq. (i),  I = 





29. 

 

Ans. Let I =   ……….(i) 
Putting 
 
 
 
From eq. (i),  I = 


30. 

 

Ans. Let I =   
 ……….(i)
Putting 
 
 
From eq. (i),  I = 


31. 

 

Ans. Let I =   
……….(i)
Putting 
 
 
From eq. (i),  I = 




32. 

 

Ans. Let I =   





Adding and subtracting   in the numerator,




 = 
where   ……….(i)
Putting 
 
 
I1 =   = 

Putting this value in eq. (i), we get required integral,

33. 

 

Ans. Let I =   





Adding and subtracting   in the numerator,


12cosxsinxcosxsinx+sinx+cosxcosxsinxdx12∫cos⁡x−sin⁡xcos⁡x−sin⁡x+sin⁡x+cos⁡xcos⁡x−sin⁡xdx
12(1+sinx+cosxcosxsinx)dx12∫(1+sin⁡x+cos⁡xcos⁡x−sin⁡x)dx


34. 

 

Ans. Let I =   


…..(i)
Putting 

 
From eq. (i), I = 




35. 

 

Ans. Let I =  ……….(i) 
Putting 
 
 
From eq. (i), I = 


36. 

 

Ans. Let I =   ……….(i) 
Putting 
 
 
 
From eq. (i), I = 


37. 

 

Ans. Let I =   
 ……….(i)
Putting 
 
 
From eq. (i), I = 


Choose the correct answer in Exercise 38 and 39.

 
38.  equals
(A) 
(B) 
(C) 
(D) log(10x+x10)+clog(10x+x10)+c

Ans. Let I =   ……….(i) 
Putting 
 
From eq. (i), I = 


Therefore, option (D) is correct.

39.   equals

 
(A) 
(B) 
(C) 
(D) 

Ans.   






Therefore, option (B) is correct.

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