SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

Q.1 Integrate:

Let  = t

∴2x dx = dt

Q. 2 Integrate:

Let log |x| = t

∴ 

Q. 3 INTEGRATE

Let 1 + log x = t

∴ 

4. Integrate : sin x ⋅ sin (cos x)

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

sin x ⋅ sin (cos x)

Let cos x = t

∴ −sin x dx = dt

5.integrate:

Let 

∴ 2adx = dt

6. integrate: Let ax + b = t⇒ adx = dt

7. Integrate:

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

Let 

∴ dx = dt

8. Integrate:

Let 1 + 2x2 = t

∴ 4xdx = dt

9. Integrate:

Let 

∴ (2x + 1)dx = dt

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

 10. Integrate:

Let 

∴

11. Integrate:

Let 

∴ dx = dt

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

12. Integrate:

Let 

∴ 

 13. Integrate:

Let 

∴ 9x2 dx = dt

 

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

14. Integrate:

Let log x = t

∴ 

15. Integrte:

Let 

∴ −8x dx = dt

16. Integrate:

Let 

∴ 2dx = dt

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

17. Integrate:

Let 

∴ 2xdx = dt

18. Integrate:

Let 

∴ 

19. Integrate:

Dividing numerator and denominator by ex, we obtain

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

Let 

∴ 

20. Integrate:

Let 

∴ 

21. Integrate: 

Let 2x − 3 = t∴ 2dx = dt

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

22. Integrate:

Let 7 − 4x = t

∴ −4dx = dt

23.Integrate:

Let 

∴ 

24. Integrate: 

Let 

∴ 

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

25. Integrate:

Let 

∴ 

 26. Integrate:

Let 

∴ 

27. Integrate:  

Let sin 2x = t∴ 

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

 28. Integrate:

Let 

∴ cos x dx = dt

29. Integrate: cot x log sin x

Let log sin x = t

30. Integrate:

Let 1 + cos x = t

∴ −sin x dx = dt

Let 1 + cos x = t

∴ −sin x dx = dt

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

31. Integrate:

32. Integrate:

Let sin x + cos x = t ⇒ (cos x − sin x) dx = dt

33. Integrate:

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

Put cos x − sin x = t ⇒ (−sin x − cos x) dx = dt

 34. Integrate:

Put cos x − sin x = t ⇒ (−sin x − cos x) dx = dt

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

35. Integrate:

Let 1 + log x = t

∴ 

36. Integrate:

Let 

∴ 

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

37. Integrate:

Let x4 = t

∴ 4x3 dx = dt

Let 

∴From (1), we obtain

From (1), we obtainFrom (1), we obtain

38. Integrate: equals

Let 

∴ 

Hence, the correct answer is D.

SOLUTIONS TO NCERT EXERCISE: CLASS XII: MATHEMATICSCOMPILED BY : M.SRINIVASAN, PGT(MATHS), ZIET, MUMBAI

39.  equals

A. B. C. D.

Hence, the correct answer is B.