NCERT Solutions for Class 12 Maths Exercise 7.10 hapter 7 Integrals – FREE PDF Download
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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)10−47(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. 
= 
= 
= 
= 
= 
= 
= 
= 
=117√log(17√+317√−3×17√+117√−1)=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.
