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# NCERT Solutions class 12 Maths 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.

## NCERT Solutions class 12 Maths Exercise 7.10

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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