NCERT Solutions for Class 12 Maths Exercise 7.2 hapter 7 Integrals – FREE PDF Download
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NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2
Integrate the functions in Exercise 1 to 8.
1. 
= 
= 
2. 
= 
= 
= 
3.
= 
=
= 
4.
= 
= 
= 
= 
= 
5.
= 
= 12∫sin2(ax+b)dx12∫sin2(ax+b)dx
= 
= 12[−cos(2ax+2b)2a]+c12[−cos(2ax+2b)2a]+c [ because∫Sin(ax+b)dx=−1aCos(ax+b)∫Sin(ax+b)dx=−1aCos(ax+b)]
= 
6.
= 
Using ∫(ax+b)ndx=(ax+b)n+1a(n+1)+c∫(ax+b)ndx=(ax+b)n+1a(n+1)+c We have
= 
= 
7.
= 
= 
= 
= 
Using ∫(ax+b)ndx=(ax+b)n+1a(n+1)+c∫(ax+b)ndx=(ax+b)n+1a(n+1)+c
= 
= 
8.
= 
……….(i)
Putting 
From eq. (i),
I = 
= 
= 
= 
= 
Integrate the functions in Exercise 9 to 17.
9. 
= 
= 
…..(i)
Putting 
From eq. (i), I = 
= 
= 
= 
= 
10.
……….(i) Putting 
From eq. (i),
I = 
= 
= 
= 
= 
11.
= 
= 
= 
= 
= 
Using ∫(ax+b)ndx=(ax+b)n+1a(n+1)+c∫(ax+b)ndx=(ax+b)n+1a(n+1)+c
= 
= 2x+4−−−−√(x+43−4)+c2x+4(x+43−4)+c
= 2x+4−−−−√(x+4−123)+c2x+4(x+4−123)+c
= 
12.
= 
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
= 
= 
= 
= 
13.
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
= 
14.
= 
……….(i)
Putting
From eq. (i), I = 
= 
= 
= 
15.
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
= 
16.
= 
Using∫eax+bdx=eax+ba+c∫eax+bdx=eax+ba+c
17.
= 
……….(i
Putting 
From eq. (i), I = 
= 
using ∫eax+bdx=eax+ba+c∫eax+bdx=eax+ba+c
We have =12(e−t−1)+c=12(e−t−1)+c
= 
= 
Integrate the functions in Exercise 18 to 26.
18. 
……….(i) Putting 
From eq. (i), I = 
= 
= 
19.
= 
[Multiplying each term by 
]
Putting 
From eq. (i), I = 
= 
= 
= 
= 
20.
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
= 
21.
= 
= 
Using ∫sec2(ax+b)dx=tan(ax+b)a+c∫sec2(ax+b)dx=tan(ax+b)a+c
=tan(2x−3)2−x+c=tan(2x−3)2−x+c
22.
Using ∫sec2(ax+b)dx=tan(ax+b)a+c∫sec2(ax+b)dx=tan(ax+b)a+c
= 
23.
……….(i) Putting 
From eq. (i), I = 
= 
= 
24.
= 
= 
……….(i)
Putting 
From eq. (i), I = =
= 
25.
= 
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
= 
= 
26.
……….(i) Putting
From eq. (i), I = 
= 
= 
=
Integrate the functions in Exercise 27 to 37.
27. 
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
= 
= 
28.
……….(i) Putting 
From eq. (i), I = 
= 
= 
= 
= 
= 
29.
……….(i) Putting 
From eq. (i), I =
=
= 
30.
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
31.
= 
……….(i)
Putting
From eq. (i), I = 
=
=
=
= 
32.
= 
= 
= 
= 
= 
Adding and subtracting 
in the numerator,
= 
= 
= 
= 
= 
= 
where 
……….(i)
Putting 
I1 = = 
= 
Putting this value in eq. (i), we get required integral,
= 
33.
= 
= 
= 
= 
= 
Adding and subtracting 
in the numerator,
= 
= 
= 12∫cosx−sinxcosx−sinx+sinx+cosxcosx−sinxdx12∫cosx−sinxcosx−sinx+sinx+cosxcosx−sinxdx
= 12∫(1+sinx+cosxcosx−sinx)dx12∫(1+sinx+cosxcosx−sinx)dx
= 
= 
34.
= 
= 
= 
…..(i)
Putting 
From eq. (i), I = 
=
= 
=
= 
35.
……….(i) Putting
From eq. (i), I =
= 
= 
36.
……….(i) Putting 
From eq. (i), I =
=
= 
37.
= 
……….(i)
Putting 
From eq. (i), I = 
= 
= 
Choose the correct answer in Exercise 38 and 39.
38. 
equals
(A) 
(B) 
(C) 
(D) log(10x+x10)+clog(10x+x10)+c
……….(i) Putting 
From eq. (i), I =
=
= 
Therefore, option (D) is correct.
39. equals
equals
(A) 
(B) 
(C) 
(D) 
= 
= 
= 
= 
= 
= 
Therefore, option (B) is correct.