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Exam: CBSE Class 12
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Q1
#1
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Write an anti derivative for each of the following functions using the method of inspection: (i)
cos
2
x
\cos 2x
cos
2
x
(ii)
3
x
2
+
4
x
3
3x^2 + 4x^3
3
x
2
+
4
x
3
(iii)
1
x
\dfrac{1}{x}
x
1
,
x
≠
0
x \neq 0
x
=
0
.
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[Q7.1 Eg.1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q2
#2
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the following integrals: (i)
∫
x
3
−
1
x
2
d
x
\int \dfrac{x^3 - 1}{x^2}\,dx
∫
x
2
x
3
−
1
d
x
(ii)
∫
(
x
2
/
3
+
1
)
d
x
\int \left(x^{2/3} + 1\right) dx
∫
(
x
2/3
+
1
)
d
x
(iii)
∫
(
x
3
/
2
+
2
e
x
−
1
x
)
d
x
\int \left(x^{3/2} + 2e^x - \dfrac{1}{x}\right) dx
∫
(
x
3/2
+
2
e
x
−
x
1
)
d
x
.
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[Q7.1 Eg.2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q3
#3
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the following integrals: (i)
∫
(
sin
x
+
cos
x
)
d
x
\int (\sin x + \cos x)\,dx
∫
(
sin
x
+
cos
x
)
d
x
(ii)
∫
csc
x
(
csc
x
+
cot
x
)
d
x
\int \csc x\,(\csc x + \cot x)\,dx
∫
csc
x
(
csc
x
+
cot
x
)
d
x
(iii)
∫
1
−
sin
x
cos
2
x
d
x
\int \dfrac{1 - \sin x}{\cos^2 x}\,dx
∫
cos
2
x
1
−
sin
x
d
x
.
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[Q7.1 Eg.3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q4
#4
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the anti derivative
F
F
F
of
f
f
f
defined by
f
(
x
)
=
4
x
3
−
6
f(x) = 4x^3 - 6
f
(
x
)
=
4
x
3
−
6
, where
F
(
0
)
=
3
F(0) = 3
F
(
0
)
=
3
.
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[Q7.1 Eg.4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q5
#5
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find an anti derivative (or integral) of the following function by the method of inspection:
sin
2
x
\sin 2x
sin
2
x
.
Show model answer
[QEx 7.1 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q6
#6
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find an anti derivative (or integral) of the following function by the method of inspection:
cos
3
x
\cos 3x
cos
3
x
.
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[QEx 7.1 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q7
#7
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find an anti derivative (or integral) of the following function by the method of inspection:
e
2
x
e^{2x}
e
2
x
.
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[QEx 7.1 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q8
#8
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find an anti derivative (or integral) of the following function by the method of inspection:
(
a
x
+
b
)
2
(ax + b)^2
(
a
x
+
b
)
2
.
Show model answer
[QEx 7.1 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q9
#9
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find an anti derivative (or integral) of the following function by the method of inspection:
sin
2
x
−
4
e
3
x
\sin 2x - 4e^{3x}
sin
2
x
−
4
e
3
x
.
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[QEx 7.1 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q10
#10
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find the integral
∫
(
4
e
3
x
+
1
)
d
x
\int \left(4e^{3x} + 1\right) dx
∫
(
4
e
3
x
+
1
)
d
x
.
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[QEx 7.1 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q11
#11
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find the integral
∫
x
2
(
1
−
1
x
2
)
d
x
\int x^2 \left(1 - \dfrac{1}{x^2}\right) dx
∫
x
2
(
1
−
x
2
1
)
d
x
.
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[QEx 7.1 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q12
#12
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find the integral
∫
(
a
x
2
+
b
x
+
c
)
d
x
\int \left(ax^2 + bx + c\right) dx
∫
(
a
x
2
+
b
x
+
c
)
d
x
.
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[QEx 7.1 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q13
#13
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find the integral
∫
(
2
x
2
+
e
x
)
d
x
\int \left(2x^2 + e^x\right) dx
∫
(
2
x
2
+
e
x
)
d
x
.
Show model answer
[QEx 7.1 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q14
#14
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
(
x
−
1
x
)
2
d
x
\int \left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)^2 dx
∫
(
x
−
x
1
)
2
d
x
.
Show model answer
[QEx 7.1 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q15
#15
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
x
3
+
5
x
2
−
4
x
2
d
x
\int \dfrac{x^3 + 5x^2 - 4}{x^2}\,dx
∫
x
2
x
3
+
5
x
2
−
4
d
x
.
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[QEx 7.1 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q16
#16
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
x
3
+
3
x
+
4
x
d
x
\int \dfrac{x^3 + 3x + 4}{\sqrt{x}}\,dx
∫
x
x
3
+
3
x
+
4
d
x
.
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[QEx 7.1 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q17
#17
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
x
3
−
x
2
+
x
−
1
x
−
1
d
x
\int \dfrac{x^3 - x^2 + x - 1}{x - 1}\,dx
∫
x
−
1
x
3
−
x
2
+
x
−
1
d
x
.
Show model answer
[QEx 7.1 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q18
#18
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
(
1
−
x
)
x
d
x
\int (1 - x)\sqrt{x}\,dx
∫
(
1
−
x
)
x
d
x
.
Show model answer
[QEx 7.1 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q19
#19
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
x
(
3
x
2
+
2
x
+
3
)
d
x
\int \sqrt{x}\left(3x^2 + 2x + 3\right) dx
∫
x
(
3
x
2
+
2
x
+
3
)
d
x
.
Show model answer
[QEx 7.1 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q20
#20
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find the integral
∫
(
2
x
−
3
cos
x
+
e
x
)
d
x
\int \left(2x - 3\cos x + e^x\right) dx
∫
(
2
x
−
3
cos
x
+
e
x
)
d
x
.
Show model answer
[QEx 7.1 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q21
#21
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
(
2
x
2
−
3
sin
x
+
5
x
)
d
x
\int \left(2x^2 - 3\sin x + 5\sqrt{x}\right) dx
∫
(
2
x
2
−
3
sin
x
+
5
x
)
d
x
.
Show model answer
[QEx 7.1 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q22
#22
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Easy
Add
Find the integral
∫
sec
x
(
sec
x
+
tan
x
)
d
x
\int \sec x\,(\sec x + \tan x)\,dx
∫
sec
x
(
sec
x
+
tan
x
)
d
x
.
Show model answer
[QEx 7.1 Q18 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q23
#23
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
sec
2
x
csc
2
x
d
x
\int \dfrac{\sec^2 x}{\csc^2 x}\,dx
∫
csc
2
x
sec
2
x
d
x
.
Show model answer
[QEx 7.1 Q19 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q24
#24
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
Find the integral
∫
2
−
3
sin
x
cos
2
x
d
x
\int \dfrac{2 - 3\sin x}{\cos^2 x}\,dx
∫
cos
2
x
2
−
3
sin
x
d
x
.
Show model answer
[QEx 7.1 Q20 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q25
#25
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
The anti derivative of
(
x
+
1
x
)
\left(\sqrt{x} + \dfrac{1}{\sqrt{x}}\right)
(
x
+
x
1
)
equals
A
1
3
x
1
/
3
+
2
x
1
/
2
+
C
\dfrac{1}{3}x^{1/3} + 2x^{1/2} + C
3
1
x
1/3
+
2
x
1/2
+
C
B
2
3
x
2
/
3
+
1
2
x
2
+
C
\dfrac{2}{3}x^{2/3} + \dfrac{1}{2}x^2 + C
3
2
x
2/3
+
2
1
x
2
+
C
C
2
3
x
3
/
2
+
2
x
1
/
2
+
C
\dfrac{2}{3}x^{3/2} + 2x^{1/2} + C
3
2
x
3/2
+
2
x
1/2
+
C
D
3
2
x
3
/
2
+
1
2
x
1
/
2
+
C
\dfrac{3}{2}x^{3/2} + \dfrac{1}{2}x^{1/2} + C
2
3
x
3/2
+
2
1
x
1/2
+
C
Tap an option to check your answer.
[QEx 7.1 Q21 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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