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Solutions ⇒ Class 12th ⇒ Mathematics-II ⇒ 7. Integrals

Solutions 7. Integrals - Exercise 7.2 | Class 12 Mathematics-II - Toppers Study

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7. Integrals

| Exercise 7.2 |

Solutions 7. Integrals - Exercise 7.2 | Class 12 Mathematics-II - Toppers Study


Exercise 7.2

Integrate the functions in Exercise 1 to 37

 

Ques.1. 

Ans. Putting 

 

 

Ques.2.  

Ans. Putting 

 

 

 

 

Ques.3.  

Ans. Putting 

 

 

 

 

Ques.4.  

Ans. Putting 

 

 

 

 

 

Ques.5. 

Ans. 

 

Ques.6.  

Ans. 

 

Ques.7.  

Ans. 

 

Ques.8.  

Ans. Let I = 

 ……….(i)

Putting 

 

From eq. (i),

I = 

 

Ques9. 

Ans. Let I = 

 …..(i)

Putting 

 

 

 From eq. (i), I = 

 

Ques.10.  

Ans. Let I = ……….(i)

Putting 

 

 

 

From eq. (i),

I = 

 

Ques.11. 

Ans. 

 

Ques.12.  

Ans. Let I = 

 ……….(i)

Putting 

 

 

From eq. (i), I = 

 

Ques.13. 

Ans. Let I = 

……….(i)

Putting 

 

From eq. (i), I = 

 

Ques.14.  

Ans. Let I = 

……….(i)

Putting 

 

 

From eq. (i), I =  = 

 

Ques.15. 

Ans. Let I = 

……….(i)

Putting 

 

 

From eq. (i), I =  = 

 

Ques.16. 

Ans.  = 

 

Ques.17.  

Ans. Let I = 

……….(i

Putting 

 

 

From eq. (i), I =  = 

 

Ques.18. 

Ans. Let I =  ……….(i)

Putting 

 

From eq. (i), I = 

Ques.19. 

Ans. Let I = 

 [Multiplying each term by ]

Putting 

 

 

From eq. (i), I =  = 

 

Ques.20. 

Ans. Let I = 

……….(i)

Putting 

 

 

 

From eq. (i), I = 

 

Ques.21. 

Ans. 

 

Ques.22. 

Ans. 

 

Ques.23 

Ans. Let I = ……….(i)

Putting 

 

 

From eq. (i), I = 

 

Ques.24.  

Ans. Let I = 

……….(i)

Putting 

 

 

From eq. (i), I =  = 

 

Ques.25.  

Ans. Let I = 

……….(i)

Putting 

 

From eq. (i),  I =  = 

 

Ques.26.  

Ans. Let I = ……….(i)

Putting 

 

 

 

From eq. (i),  I = 

=

 

Ques.27.  

Ans. Let I = 

 ……….(i)

Putting 

 

 

From eq. (i),  I = 

 

Ques.28. 

Ans. Let I = ……….(i)

Putting 

 

 

From eq. (i),  I = 

 

Ques.29. 

Ans. Let I =  ……….(i)

Putting 

 

 

   

From eq. (i),  I = 

 

Ques.30.  

Ans. Let I = 

 ……….(i)

Putting 

 

 

From eq. (i),  I = 

 

Ques.31.  

Ans. Let I = 

……….(i)

Putting 

 

 

From eq. (i),  I = 

 

Ques.32.  

Ans. Let I = 

Adding and subtracting  in the numerator,

 = 

where  ……….(i)

Putting 

 

 

I1 =  = 

Putting this value in eq. (i)

 

Ques.33. 

Ans. Let I = 

Adding and subtracting  in the numerator,

 

Ques34. 

Ans. Let I = 

…..(i)

Putting 

 

From eq. (i), I = 

 

Ques.35

Ans. Let I = ……….(i)

Putting 

 

 

From eq. (i), I = 

 

Ques.36. 

Ans. Let I =  ……….(i)

Putting 

 

 

 

From eq. (i), I = 

 

Ques.37.  

Ans. Let I = 

 ……….(i)

Putting 

 

 

From eq. (i), I = 

Choose the correct answer in Exercise 38 and 39.

 

Ques38.  equals

(A) 

(B)  

(C) 

(D) 

Ans. Let I =  ……….(i)

Putting 

 

From eq. (i), I = 

hance, option (D) is correct.

 

Ques.39.  equals

(A) 

(B)  

(C) 

(D) 

Ans. 

hance, option (B) is correct.

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