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CBSE And NCERT Solutions:

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

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NCERT SolutionsClass 12th Mathematics-II Chapter 7. Integrals:
Page 3 of 12

7. Integrals

 

Exercise 7.3

 

Exersice 7.3

Find the integrals of the following functions in Exercises 1 to 9.

Ques.1. 

Ans. 

 

Ques.2. 

Ans.   = 

 

Ques.3.  

Ans. 

 

Ques.4. 

Ans. 

 

Ques.5. 

Ans. 

 

Ques.6.  

Ans. 

 

Ques.7. 

Ans. 

 

Ques.8. 

Ans. 

 

Ques.9.  

Ans. 

Find the integrals of the following functions in Exercises 10 to 18.

 

Ques.10.  

Ans. 

 

Ques.11. 

Ans. 

 

Ques12.  

Ans. 

 

Ques.13.  

Ans. 

 

Ques.14. 

Ans. Let I

 …..(i)

Putting 

 

 

 From eq. (i), I = 

 

Ques.15.  

Ans. Let I

Putting 

 

 

 From eq. (i),

I = 

 

Ques.16.  

Ans. 

……….(i)

Putting 

 

 

 From eq. (i),

 

Ques.17.  

Ans. 

 

Ques.18.  

Ans. 

Integrate the following functions in Exercises 19 to 22.

 

Ques.19. 

Ans. Let I ……….(i)

Here  is a negative even integer.

Therefore, multiplying both numerator and denominator by 

I = 

 ……….(ii)

Putting 

 

 

 From eq. (ii),

I = 

 

Ques.20.  

Ans. Let I

 ……….(i)

Putting 

 

 

 From eq. (i),

I = 

 

Ques.21.  

Ans. 

 

Ques.22.  

Ans. Let I  ……….(i)

Multiplying and dividing by  as ,

I = 

Choose the correct answer in Exercise 23 and 24.

 

Ques.23.  is equal to:

(A)  

(B)  

(C)  

(D) 

Ans. 

hance, option (A) is correct.

 

Ques.24.  is equal to:

(A)  

(B) 

(C)  

(D) 

Ans. Let I =  ……….(i)

Putting 

 

 

 From eq. (i),

I = 

hance, option (B) is correct.

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