NCERT Solutions for Class 12 Maths Exercise 7.1 hapter 7 Integrals – FREE PDF Download
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NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.1) Exercise 7.1
Find an antiderivative (or integral) of the following functions by the method of inspection in Exercises 1 to 5.
1. 
An anti-derivative of is 
2. 
An anti-derivative of 
is 
3.
An anti-derivative of 
is 
4. (ax+b)2(ax+b)2
An anti-derivative of 
is 
5.
…..(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. 
= 
= 
= 
7.
= 
= 
= 
8.
= 
= 
= 
where 
is the constant of integration.
9.
= 
= 
= 
10.
= ∫{(x−−√)2+(1x√)2−2x−−√1x√}dx∫{(x)2+(1x)2−2x1x}dx
= 
= 
= 
11.
= 
= 
= 
= 
= 
Evaluate the following integrals in Exercises 12 to 16.
12. 
= 
= 
= 
= 
= 
= 
= 
13.
= 
= 
= 
= 
= 
14.
= 
= 
= 
= 
= 
= 
15.
= 
= 
= 
= 
= 
= 
16.
= 
= 
= 
= 
Evaluate the following integrals in Exercises 17 to 20.
17. 
= 
= 
= 
= 
18.
= 
= 
= 
19.
= 
= 
= 
= 
= 
= 
20.
= 
= 
= 
= 
21. Choose the correct answer:
The anti derivative of 
equals.
(A) 
(B) 
(C) 
(D) 
= 
= 
= 
= 
= 
Therefore, option (C) is correct.
22. Choose the correct answer:
If 
such that 
Then 
is:
(A) 
(B) 
(C) 
(D) 
= 
= 
= 
……….(i)
Putting in eq. (i),
Therefore, option (A) is correct.
