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Exam: CBSE Class 12
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Q76
#76
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
x
9
−
4
x
2
\dfrac{x}{9 - 4x^2}
9
−
4
x
2
x
.
Show model answer
[QEx 7.2 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q77
#77
Mathematics → Integrals → Integration by Substitution
·
Easy
Add
Integrate the function
e
2
x
+
3
e^{2x + 3}
e
2
x
+
3
.
Show model answer
[QEx 7.2 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q78
#78
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
x
e
x
2
\dfrac{x}{e^{x^2}}
e
x
2
x
.
Show model answer
[QEx 7.2 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q79
#79
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
e
tan
−
1
x
1
+
x
2
\dfrac{e^{\tan^{-1} x}}{1 + x^2}
1
+
x
2
e
t
a
n
−
1
x
.
Show model answer
[QEx 7.2 Q18 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q80
#80
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
e
2
x
−
1
e
2
x
+
1
\dfrac{e^{2x} - 1}{e^{2x} + 1}
e
2
x
+
1
e
2
x
−
1
.
Show model answer
[QEx 7.2 Q19 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q81
#81
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
e
2
x
−
e
−
2
x
e
2
x
+
e
−
2
x
\dfrac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}}
e
2
x
+
e
−
2
x
e
2
x
−
e
−
2
x
.
Show model answer
[QEx 7.2 Q20 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q82
#82
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
tan
2
(
2
x
−
3
)
\tan^2 (2x - 3)
tan
2
(
2
x
−
3
)
.
Show model answer
[QEx 7.2 Q21 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q83
#83
Mathematics → Integrals → Integration by Substitution
·
Easy
Add
Integrate the function
sec
2
(
7
−
4
x
)
\sec^2 (7 - 4x)
sec
2
(
7
−
4
x
)
.
Show model answer
[QEx 7.2 Q22 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q84
#84
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
sin
−
1
x
1
−
x
2
\dfrac{\sin^{-1} x}{\sqrt{1 - x^2}}
1
−
x
2
sin
−
1
x
.
Show model answer
[QEx 7.2 Q23 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q85
#85
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
2
cos
x
−
3
sin
x
6
cos
x
+
4
sin
x
\dfrac{2 \cos x - 3 \sin x}{6 \cos x + 4 \sin x}
6
cos
x
+
4
sin
x
2
cos
x
−
3
sin
x
.
Show model answer
[QEx 7.2 Q24 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q86
#86
Mathematics → Integrals → Integration by Substitution
·
Hard
Add
Integrate the function
1
cos
2
x
(
1
−
tan
x
)
2
\dfrac{1}{\cos^2 x (1 - \tan x)^2}
cos
2
x
(
1
−
tan
x
)
2
1
.
Show model answer
[QEx 7.2 Q25 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q87
#87
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
cos
x
x
\dfrac{\cos \sqrt{x}}{\sqrt{x}}
x
cos
x
.
Show model answer
[QEx 7.2 Q26 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q88
#88
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
sin
2
x
cos
2
x
\sqrt{\sin 2x}\, \cos 2x
sin
2
x
cos
2
x
.
Show model answer
[QEx 7.2 Q27 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q89
#89
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
cos
x
1
+
sin
x
\dfrac{\cos x}{\sqrt{1 + \sin x}}
1
+
sin
x
cos
x
.
Show model answer
[QEx 7.2 Q28 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q90
#90
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
cot
x
log
sin
x
\cot x \log \sin x
cot
x
lo
g
sin
x
.
Show model answer
[QEx 7.2 Q29 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q91
#91
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
sin
x
1
+
cos
x
\dfrac{\sin x}{1 + \cos x}
1
+
cos
x
sin
x
.
Show model answer
[QEx 7.2 Q30 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q92
#92
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
sin
x
(
1
+
cos
x
)
2
\dfrac{\sin x}{(1 + \cos x)^2}
(
1
+
cos
x
)
2
sin
x
.
Show model answer
[QEx 7.2 Q31 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q93
#93
Mathematics → Integrals → Integration by Substitution
·
Hard
Add
Integrate the function
1
1
+
cot
x
\dfrac{1}{1 + \cot x}
1
+
cot
x
1
.
Show model answer
[QEx 7.2 Q32 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q94
#94
Mathematics → Integrals → Integration by Substitution
·
Hard
Add
Integrate the function
1
1
−
tan
x
\dfrac{1}{1 - \tan x}
1
−
tan
x
1
.
Show model answer
[QEx 7.2 Q33 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q95
#95
Mathematics → Integrals → Integration by Substitution
·
Hard
Add
Integrate the function
tan
x
sin
x
cos
x
\dfrac{\sqrt{\tan x}}{\sin x \cos x}
sin
x
cos
x
tan
x
.
Show model answer
[QEx 7.2 Q34 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q96
#96
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
Integrate the function
(
1
+
log
x
)
2
x
\dfrac{(1 + \log x)^2}{x}
x
(
1
+
lo
g
x
)
2
.
Show model answer
[QEx 7.2 Q35 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q97
#97
Mathematics → Integrals → Integration by Substitution
·
Hard
Add
Integrate the function
(
x
+
1
)
(
x
+
log
x
)
2
x
\dfrac{(x + 1)(x + \log x)^2}{x}
x
(
x
+
1
)
(
x
+
lo
g
x
)
2
.
Show model answer
[QEx 7.2 Q36 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q98
#98
Mathematics → Integrals → Integration by Substitution
·
Hard
Add
Integrate the function
x
3
sin
(
tan
−
1
x
4
)
1
+
x
8
\dfrac{x^3 \sin (\tan^{-1} x^4)}{1 + x^8}
1
+
x
8
x
3
sin
(
tan
−
1
x
4
)
.
Show model answer
[QEx 7.2 Q37 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q99
#99
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
∫
10
x
9
+
10
x
log
e
10
x
10
+
10
x
d
x
\displaystyle\int \dfrac{10x^9 + 10^x \log_e 10}{x^{10} + 10^x}\,dx
∫
x
10
+
1
0
x
10
x
9
+
1
0
x
lo
g
e
10
d
x
equals
A
10
x
−
x
10
+
C
10^x - x^{10} + C
1
0
x
−
x
10
+
C
B
10
x
+
x
10
+
C
10^x + x^{10} + C
1
0
x
+
x
10
+
C
C
(
10
x
−
x
10
)
−
1
+
C
(10^x - x^{10})^{-1} + C
(
1
0
x
−
x
10
)
−
1
+
C
D
log
(
10
x
+
x
10
)
+
C
\log (10^x + x^{10}) + C
lo
g
(
1
0
x
+
x
10
)
+
C
Tap an option to check your answer.
[QEx 7.2 Q38 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q100
#100
Mathematics → Integrals → Integration by Substitution
·
Moderate
Add
∫
d
x
sin
2
x
cos
2
x
\displaystyle\int \dfrac{dx}{\sin^2 x \cos^2 x}
∫
sin
2
x
cos
2
x
d
x
equals
A
tan
x
+
cot
x
+
C
\tan x + \cot x + C
tan
x
+
cot
x
+
C
B
tan
x
−
cot
x
+
C
\tan x - \cot x + C
tan
x
−
cot
x
+
C
C
tan
x
cot
x
+
C
\tan x \cot x + C
tan
x
cot
x
+
C
D
tan
x
−
cot
2
x
+
C
\tan x - \cot 2x + C
tan
x
−
cot
2
x
+
C
Tap an option to check your answer.
[QEx 7.2 Q39 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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