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NCERT Solutions class 12 Maths Exercise 7.10 (Ex 7.10) Chapter 7 Integrals

NCERT Solutions for Class 12 Maths Exercise 7.10 hapter 7 Integrals – FREE PDF Download

NCERT Solutions for integrals Class 12 exercises 7.10 are accessible in PDF format which is available at CoolGyan’s online learning portal. The solutions to this particular exercise from chapter 7 Integrals have been prepared by our experts who have years of experience in this field. Students can find, well-explained solutions to maths problems at CoolGyan’s online learning portal. All the solutions are provided in a way that will help you in understanding the concept effectively. You can download them in PDF format for free.

NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.10) Exercise 7.10



Evaluate the integrals in Exercises 1 to 8 using substitutions.

1.  

Ans. Let I = 

 ……….(i)

Putting 

  

 

To change the limits of integration from x to t

when x = 0, t = x2 +1 = 0 +1 = 1

when x =1, t = x2 +1 = 1 +1 = 2

  From eq. (i),

 Ans.


2. 

Ans. Let I =  ……….(i)

Putting 

 

 

To change the limits of integration from  to 

When 

When 

  From eq. (i),

I = 

=23(t32)10+211(t112)1047(t72)10=23(t32)01+211(t112)01−47(t72)01

 Ans.


3.  

Ans. Let I =  ……….(i)

Putting 

 

 

Limits of integration, when  

when 

 

  From eq. (i),

I = 

[Applying Product Rule]

 Ans.


4.  

Ans. Let I =  ……….(i)

Putting 

 

 

 

Limits of integration when  and when 

  From eq. (i),

I = 

 Ans.


5. 

Ans. Let I = 

 ……….(i)

Putting 

  

 

Limits of integration when  and when 

  From eq. (i), I = 

 Ans.


6. 

Ans. 

=117log(17+3173×17+1171)=117log⁡(17+317−3×17+117−1)

 Ans.


7. 

Ans. Let I = 

……….(i)

Putting 

  

 

Limits of integration when  and when 

  From eq. (i), I = 

 Ans.


8.  

Ans. Let I =  ……….(i)

Putting 

 

 

 

Limits of integration when  and when 

  From eq. (i),

I = 

=(ett)42=(ett)24

 Ans.


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.