# NCERT Solutions for Class 12 Mathematics-II english Medium 7. Integrals

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##### NCERT Solutions⇒Class 12th ⇒ Mathematics-II ⇒ Chapter 7. Integrals:

## 7. Integrals

#### Exercise 7.9

**Exercise - 7.9**

**Evaluate the definite integrals in Exercises 1 to 20**

**Ques.1. **

**Ans. **

=

=

=

=

=

= 2

**Ques.2. **

**Ans. **

=

=

=

=

=

**Ques.3. **

**Ans. **

=

=

=

=

=

=

=

= =

**Ques.4. **

**Ans. **

=

=

=

= =

**Ques.5. **

**Ans. **

=

=

= = 0

**Ques.6. **

**Ans. **

=

=

=

**Ques.7. **

**Ans. **

=

=

=

=

=

=

**Ques.8. **

**Ans. **

=

=

=

=

=

**Ques.9. **

**Ans. **

=

=

= =

**Ques.10. **

**Ans. **

=

=

= =

**Ques.11. **

**Ans. ** =

=

=

=

=

=

=

**Ques.12. **

**Ans. **

=

=

=

=

=

=

**Ques.13. **

**Ans. ** =

=

=

=

=

=

**Ques.14. **

**Ans. **

=

=

=

=

=

=

**Ques.15. **

**Ans. **

First we evaluate = ……….(i)

Putting

From eq. (i), =

=

=

=

**Ques.16. **

**Ans. **

=

= (On dividing)

=

= where I =

= ……….(i)

Now, I = ……….(ii)

Let ……….(iii)

Comparing coefficients of A + B = –20 ……….(iv)

Comparing constants 3A + B = –15 ……….(v)

On solving eq. (iv) and (v), we get A = B =

Putting these values in eq. (iii),

I =

=

=

=

=

=

Putting this value of I in eq. (i),

=

=

**Ques.17. **

**Ans. **

=

=

=

=

=

**Ques.18. **

**Ans. **

=

=

=

=

=

=

**Ques.19. **

**Ans. **

=

=

=

=

=

=

=

**Ques.20. **

**Ans. **

=

=

[Applying Product Rule on first definite integral]

=

=

=

=

=

**Choose the correct answer in Exercises 21 and 22.**

**Ques.21. equals:**

**(A) **

**(B) **

**(C) **

**(D) **

**Ans. **

=

=

= =

hance, option (D) is correct.

**Ques.22. equals:**

**(A) **

**(B) **

**(C) **

**(D) **

**Ans. **

=

=

=

=

=

=

hance, option (C) is correct.

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##### NCERT Solutions⇒Class 12th ⇒ Mathematics-II ⇒ Chapter 7. Integrals:

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