Exercise 7.10

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NCERT Solutions class 12 Maths Integrals

Evaluate the integrals in Exercises 1 to 8 using substitutions.

1.  

Ans. Let I =

=  ……….(i)

Putting

  From eq. (i),

I

=

=

=

=

=

2.

Ans. Let I =  ……….(i)

Putting

To change the limits of integration from  to

When

When

  From eq. (i),

I =

=

=

=

=

=

=

=

=

=

=

=

=

3.  

Ans. Let I =  ……….(i)

Putting

Limits of integration, when  

when

  From eq. (i),

I =

=

=

=

=

[Applying Product Rule]

=

=

=

=

=

=

=

4.  

Ans. Let I =  ……….(i)

Putting

Limits of integration when  and when

  From eq. (i),

I =

=

=

=

=

=

=

=

=

=

5.

Ans. Let I =

=  ……….(i)

Putting

Limits of integration when  and when

  From eq. (i), I =

=

=

=

=

6.

Ans.

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

7.

Ans. Let I =

=

= ……….(i)

Putting

Limits of integration when  and when

  From eq. (i), I =

=

=

=

=

8.  

Ans. Let I =  ……….(i)

Putting

Limits of integration when  and when

  From eq. (i),

I =

=

=

=

=

=

=

=

=

NCERT Solutions class 12 Maths Exercise 7.10

Choose the correct answer in Exercises 9 and 10.

9.  The value of the integral  is:

(A) 6

(B) 0

(C) 3

(D) 4

Ans. Let I =

=

=

=

=

= ……….(i)

Putting

Limits of integration when  and when

  From eq. (i),

I =

=

=

=

=

=

Therefore, option (A) is correct.

10. If  then  is:

(A)

(B)

(C)

(D)  

Ans.  

=

[Applying Product Rule]

=

=

=

=

=

Therefore, option (B) is correct.