NCERT Solutions for Class 12 Maths Exercise 7.6 hapter 7 Integrals – FREE PDF Download
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NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.6) Exercise 7.6
Integrate the functions in Exercises 1 to 8.
1. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
= 
Ans.
2. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
= 
= −x3xcos3x+19sin3x+c−x3xcos3x+19sin3x+c Ans.
3. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
[Again applying product rule]
= 
= 
= 
= 
= 
Ans.
4. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
= 
= 
Ans.
5. 
Ans. 
= 
= 
[Applying product rule]
= 
= 
= 
= 
Ans.
6. 
Ans. 
= 
= 
[Applying product rule]
= 
= 
= 
= 
Ans.
7. 
Ans. Let I = 
Putting 
I = 
= 
=12∫θ.sin2θ dθ=12∫θ.sin2θ dθ
= 
[Integrating by parts]
= 
= 
= 
= 
= 
Ans.
8. 
Ans. Let I = 
= 
= 
= 
=x22tan−1x−12∫x2+1−1x2+1dx=x22tan−1x−12∫x2+1−1×2+1dx
=x22tan−1x−12∫(1−1x2+1)dx=x22tan−1x−12∫(1−1×2+1)dx
= 
= 
=x22tan−1x−x2+12tan−1x+c Ans.=x22tan−1x−x2+12tan−1x+c Ans.
Integrate the functions in Exercises 9 to 15.
9. 
Ans. Let I = 
……….(i)
Putting 
From eq. (i),
I = 
= 
=−12∫θ.sin2θ dθ=−12∫θ.sin2θ dθ
[Applying product rule]
= 
= 
= 
= 
= 
Putting 
and 
= 
= 
Ans.
10. 
Ans. Putting
= 
[Applying product rule]
= 
= 
[Again applying product rule]
= 
= 
= 
= 
Ans.
11. 
Ans. Let I = 
……….(i)
Putting
From eq. (i),
I = 
=−∫θ.cosθ.sinθsinθdθ=−∫θ.cosθ.sinθsinθdθ
=−∫θ.cosθ dθ=−∫θ.cosθ dθ
[Applying product rule]
= 
= 
= 
= 
= 
= 
Ans.
12. 
Ans. 
[Applying product rule]
= 
= 
= 
= 
= 
Ans.
13. 
Ans. Let I = 
= 
= 
= 
=
= 
14. 
Ans. 
= 
= 
= 
= 
= 
= 
= 
= 
Ans.
15. 
Ans. 
= 
[Applying product rule]
= 
=(x33+x)logx−∫(x23+1)dx=(x33+x)logx−∫(x23+1)dx
= 
= 
= 
Ans.
Integrate the functions in Exercises 16 to 22.
16. 
Ans. Let I = 
It is in the form of 
since here 
and 
I = 
17. 
Ans. Let I = 
= 
= 
I = 
It is in the form of since here 
and 
I = 
18. 
Ans. Let I = 
= 
= 
= 
= ∫ex(tanx2+12sec2x2)dx∫ex(tanx2+12sec2x2)dx
It is in the form of since here 
and 
= 
19. 
Ans. Let I = 
It is in the form of since here 
and 
I = 
= 
20. 
Ans. Let I = 
= 
= 
I = 
It is in the form of since here 
and 
= 
= 
.
I = 
Ans.
21. 
Ans. Let I = 
[Applying product rule]
= 
I = 
[Again applying product rule]
I = 
I = 
= 
5I = 
I = 
Ans.
22. 
Ans. Putting 
= 
= 
= 
= 
[Applying product rule]
= 
= 
= 
= 
= 
= 
Ans.
Choose the correct answer in Exercise 23 and 24.
23. 
equals to
(A) 
(B) 
(C) 
(D) 
Ans. Let I =
= 
……….(i)
Putting 
From eq. (i), I = 
= 
=
Therefore, option (A) is correct.
24. 
equals:
(A) 
(B) 
(C) 
(D) 
Ans. Let I =
= 
It is in the form of since here 
and 
I = 
Therefore, option (B) is correct.
