Exercise 7.1

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NCERT Solutions class 12 Maths Integrals

Find an antiderivative (or integral) of the following functions by the method of inspection in Exercises 1 to 5.

1.  

Ans.

  An anti-derivative of  is

2.

Ans.

  An anti-derivative of  is

3.  

Ans.  

 An anti-derivative of  is

4.  

Ans.  

 An anti-derivative of  is

5.  

Ans.

  …..(i)

Again

  [Multiplying both sides by ] ……….(ii)

Adding eq. (i) and (ii), we get

 An anti-derivative of  is

Evaluate the following integrals in Exercises 6 to 11.

6.   

Ans.

=

=

=  

7.

Ans.  =  =  =

8.  

Ans.

=

=

=  where  is the constant of integration.

9.  

Ans.

=

=

=

10.

Ans.

=

=

=

=  

11.  

Ans.

=

=

=

=

=

Evaluate the following integrals in Exercises 12 to 16.

12.

Ans.

=

=

=

=

=

=

=

13.

Ans.

=

=

=

=

=

14.  

Ans.

=

=

=

=

=  =

15.  

Ans.

=

=

=

=

=

=

16.  

Ans.

=

=

=

=

NCERT Solutions class 12 Maths Exercise 7.1

Evaluate the following integrals in Exercises 17 to 20.

17. 

Ans.

=

=

=

=

18.  

Ans.

=

=

=

19.  

Ans.

=

=

=

=

=

=

20.   

Ans.

=

=

=

=

NCERT Solutions class 12 Maths Exercise 7.1

21. Choose the correct answer:

The anti derivative of  equals.

(A)  

(B)

(C)

(D)

Ans.

=

=

=

=

=

Therefore, option (C) is correct.

NCERT Solutions class 12 Maths Exercise 7.1

22. Choose the correct answer:

If  such that  Then  is:

(A)  

(B)

(C)

(D)

Ans.

=

=

=

   ……….(i)

Putting  in eq. (i),

Therefore, option (A) is correct.