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

Solutions 7. Integrals - Exercise 7.6 | Class 12 Mathematics-II - Toppers Study

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7. Integrals

| Exercise 7.6 |

Solutions 7. Integrals - Exercise 7.6 | Class 12 Mathematics-II - Toppers Study


Exercise 7.6

Integrate the functions in Exercises 1 to 22.

Ques.1.  

Ans. 

[By product rule]

 

Ques.2. 

Ans. 

[By product rule]

 

Ques.3.  

Ans. 

[By product rule]

[Again By product rule]

 

Ques.4. 

Ans. 

[By product rule]

 

Ques.5. 

Ans. 

[By product rule]

 

Ques.6 

Ans. 

[BY product rule]

 

Ques.7. 

Ans. Let I = 

Putting 

  

  I = 

[Integrating by parts]

 

Ques.8.  

Ans. Let I = 

 

Ques.9. 

Ans. Let I =  ……….(i)

Putting 

  

 

 

  From eq. (i),

I = 

[Applying product rule]

Putting  and 

 

Ques.10. 

Ans. Putting     

  

[By product rule]

[Again By product rule]

 

Ques.11.  

Ans. Let I ……….(i)

Putting 

  

 

 

  From eq. (i),

I = 

[By product rule]

 

Ques.12.  

Ans. 

[By product rule]

 

Ques.13.  

Ans. Let I

=

 

Ques.14.  

Ans. 

=  

 

Ques.15. 

Ans. 

[By product rule]

 

Ques.16. 

Ans. Let I = 

It is in the form of  since,

here  and 

  I = 

 

Ques.17.  

Ans. Let I = 

I = 

It is in the form of  since,

here  and 

I = 

 

Ques.18.  

Ans. Let I = 

It is in the form of  since,

here  and 

 

Ques.19.  

Ans. Let I = 

It is in the form of  since,

here  and 

 I = 

 

Ques.20.  

Ans. Let I = 

 I = 

It is in the form of  since,

here  and 

.

 I = 

 

Ques.21 

Ans. Let I = 

[By product rule]

  I = 

  I = 

[Again By product rule]

  I = 

  5I = 

  I = 

 

Ques.22.  

Ans. Putting 

 

  

 = 

[By product rule]

Choose the correct answer in Exercise 23 and 24.

 

Ques.23.  equals to

(A)  

(B) 

(C) 

(D) 

Ans. Let I = 

   ……….(i)

Putting 

 

 

  From eq. (i), I = 

hance, option (B) is correct.


Ques.24.  equals:

(A) 

(B) 

(C) 

(D) 

Ans. Let I = 

It is in the form of  since,

here  and 

 I = 

hance, option (B) is correct.

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