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CBSE And NCERT Solutions:

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

Select Your Subject: CBSE English Medium

 

NCERT SolutionsClass 12th Mathematics-II Chapter 7. Integrals:
Page 9 of 12

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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