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Exam: CBSE Class 12
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Set · 3 questions
Find the following integrals.
Q101
#101
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find
∫
cos
2
x
d
x
\int \cos^2 x\,dx
∫
cos
2
x
d
x
.
Show model answer
[Q7.3 Eg.7(i) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q102
#102
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find
∫
sin
2
x
cos
3
x
d
x
\int \sin 2x \cos 3x\,dx
∫
sin
2
x
cos
3
x
d
x
.
Show model answer
[Q7.3 Eg.7(ii) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q103
#103
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find
∫
sin
3
x
d
x
\int \sin^3 x\,dx
∫
sin
3
x
d
x
.
Show model answer
[Q7.3 Eg.7(iii) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q104
#104
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
sin
2
(
2
x
+
5
)
\sin^2 (2x + 5)
sin
2
(
2
x
+
5
)
.
Show model answer
[QEx 7.3 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q105
#105
Mathematics → Integrals → Integration using Trigonometric Identities
·
Easy
Add
Find the integral of
sin
3
x
cos
4
x
\sin 3x \cos 4x
sin
3
x
cos
4
x
.
Show model answer
[QEx 7.3 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q106
#106
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
cos
2
x
cos
4
x
cos
6
x
\cos 2x \cos 4x \cos 6x
cos
2
x
cos
4
x
cos
6
x
.
Show model answer
[QEx 7.3 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q107
#107
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
sin
3
(
2
x
+
1
)
\sin^3 (2x + 1)
sin
3
(
2
x
+
1
)
.
Show model answer
[QEx 7.3 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q108
#108
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
sin
3
x
cos
3
x
\sin^3 x \cos^3 x
sin
3
x
cos
3
x
.
Show model answer
[QEx 7.3 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q109
#109
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
sin
x
sin
2
x
sin
3
x
\sin x \sin 2x \sin 3x
sin
x
sin
2
x
sin
3
x
.
Show model answer
[QEx 7.3 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q110
#110
Mathematics → Integrals → Integration using Trigonometric Identities
·
Easy
Add
Find the integral of
sin
4
x
sin
8
x
\sin 4x \sin 8x
sin
4
x
sin
8
x
.
Show model answer
[QEx 7.3 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q111
#111
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
1
−
cos
x
1
+
cos
x
\dfrac{1 - \cos x}{1 + \cos x}
1
+
cos
x
1
−
cos
x
.
Show model answer
[QEx 7.3 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q112
#112
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
cos
x
1
+
cos
x
\dfrac{\cos x}{1 + \cos x}
1
+
cos
x
cos
x
.
Show model answer
[QEx 7.3 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q113
#113
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
sin
4
x
\sin^4 x
sin
4
x
.
Show model answer
[QEx 7.3 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q114
#114
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
cos
4
2
x
\cos^4 2x
cos
4
2
x
.
Show model answer
[QEx 7.3 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q115
#115
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
sin
2
x
1
+
cos
x
\dfrac{\sin^2 x}{1 + \cos x}
1
+
cos
x
sin
2
x
.
Show model answer
[QEx 7.3 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q116
#116
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
cos
2
x
−
cos
2
α
cos
x
−
cos
α
\dfrac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha}
cos
x
−
cos
α
cos
2
x
−
cos
2
α
.
Show model answer
[QEx 7.3 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q117
#117
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
cos
x
−
sin
x
1
+
sin
2
x
\dfrac{\cos x - \sin x}{1 + \sin 2x}
1
+
sin
2
x
cos
x
−
sin
x
.
Show model answer
[QEx 7.3 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q118
#118
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
tan
3
2
x
sec
2
x
\tan^3 2x \sec 2x
tan
3
2
x
sec
2
x
.
Show model answer
[QEx 7.3 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q119
#119
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
tan
4
x
\tan^4 x
tan
4
x
.
Show model answer
[QEx 7.3 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q120
#120
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
sin
3
x
+
cos
3
x
sin
2
x
cos
2
x
\dfrac{\sin^3 x + \cos^3 x}{\sin^2 x \cos^2 x}
sin
2
x
cos
2
x
sin
3
x
+
cos
3
x
.
Show model answer
[QEx 7.3 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q121
#121
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
cos
2
x
+
2
sin
2
x
cos
2
x
\dfrac{\cos 2x + 2\sin^2 x}{\cos^2 x}
cos
2
x
cos
2
x
+
2
sin
2
x
.
Show model answer
[QEx 7.3 Q18 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q122
#122
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
1
sin
x
cos
3
x
\dfrac{1}{\sin x \cos^3 x}
sin
x
cos
3
x
1
.
Show model answer
[QEx 7.3 Q19 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q123
#123
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
cos
2
x
(
cos
x
+
sin
x
)
2
\dfrac{\cos 2x}{(\cos x + \sin x)^2}
(
cos
x
+
sin
x
)
2
cos
2
x
.
Show model answer
[QEx 7.3 Q20 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q124
#124
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
Find the integral of
sin
−
1
(
cos
x
)
\sin^{-1} (\cos x)
sin
−
1
(
cos
x
)
.
Show model answer
[QEx 7.3 Q21 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q125
#125
Mathematics → Integrals → Integration using Trigonometric Identities
·
Hard
Add
Find the integral of
1
cos
(
x
−
a
)
cos
(
x
−
b
)
\dfrac{1}{\cos (x - a) \cos (x - b)}
cos
(
x
−
a
)
cos
(
x
−
b
)
1
.
Show model answer
[QEx 7.3 Q22 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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