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Exam: Maharashtra HSC Class 12
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Set · 18 questions
Evaluate the following :
Q101
#101
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
2
⋅
tan
−
1
x
d
x
\int x^2 \cdot \tan^{-1} x\, dx
∫
x
2
⋅
tan
−
1
x
d
x
Show model answer
[QEx 3.3 I (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q102
#102
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
3
⋅
tan
−
1
x
d
x
\int x^3 \cdot \tan^{-1} x\, dx
∫
x
3
⋅
tan
−
1
x
d
x
Show model answer
[QEx 3.3 I (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q103
#103
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
(
log
x
)
2
d
x
\int (\log x)^2\, dx
∫
(
lo
g
x
)
2
d
x
Show model answer
[QEx 3.3 I (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q104
#104
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
sec
3
x
d
x
\int \sec^3 x\, dx
∫
sec
3
x
d
x
Show model answer
[QEx 3.3 I (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q105
#105
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
⋅
sin
2
x
d
x
\int x \cdot \sin^2 x\, dx
∫
x
⋅
sin
2
x
d
x
Show model answer
[QEx 3.3 I (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q106
#106
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
3
⋅
log
x
d
x
\int x^3 \cdot \log x\, dx
∫
x
3
⋅
lo
g
x
d
x
Show model answer
[QEx 3.3 I (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q107
#107
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
2
x
⋅
cos
3
x
d
x
\int e^{2x} \cdot \cos 3x\, dx
∫
e
2
x
⋅
cos
3
x
d
x
Show model answer
[QEx 3.3 I (x) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q108
#108
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
⋅
sin
−
1
x
d
x
\int x \cdot \sin^{-1} x\, dx
∫
x
⋅
sin
−
1
x
d
x
Show model answer
[QEx 3.3 I (xi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q109
#109
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
2
⋅
cos
−
1
x
d
x
\int x^2 \cdot \cos^{-1} x\, dx
∫
x
2
⋅
cos
−
1
x
d
x
Show model answer
[QEx 3.3 I (xii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q110
#110
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
log
(
log
x
)
x
d
x
\int \frac{\log (\log x)}{x}\, dx
∫
x
l
o
g
(
l
o
g
x
)
d
x
Show model answer
[QEx 3.3 I (xiii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q111
#111
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
t
sin
−
1
t
1
−
t
2
d
t
\int \frac{t \sin^{-1} t}{\sqrt{1 - t^2}}\, dt
∫
1
−
t
2
t
s
i
n
−
1
t
d
t
Show model answer
[QEx 3.3 I (xiv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q112
#112
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
cos
x
d
x
\int \cos \sqrt{x}\, dx
∫
cos
x
d
x
Show model answer
[QEx 3.3 I (xv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q113
#113
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
sin
θ
⋅
log
(
cos
θ
)
d
θ
\int \sin \theta \cdot \log (\cos \theta)\, d\theta
∫
sin
θ
⋅
lo
g
(
cos
θ
)
d
θ
Show model answer
[QEx 3.3 I (xvi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q114
#114
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
⋅
cos
3
x
d
x
\int x \cdot \cos^3 x\, dx
∫
x
⋅
cos
3
x
d
x
Show model answer
[QEx 3.3 I (xvii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q115
#115
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
sin
(
log
x
)
2
x
⋅
log
x
d
x
\int \frac{\sin (\log x)^2}{x} \cdot \log x\, dx
∫
x
s
i
n
(
l
o
g
x
)
2
⋅
lo
g
x
d
x
Show model answer
[QEx 3.3 I (xviii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q116
#116
Mathematics → Indefinite Integration → Integration by Parts
·
Easy
Add
∫
log
x
x
d
x
\int \frac{\log x}{x}\, dx
∫
x
l
o
g
x
d
x
Show model answer
[QEx 3.3 I (xix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q117
#117
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
x
⋅
sin
2
x
⋅
cos
5
x
d
x
\int x \cdot \sin 2x \cdot \cos 5x\, dx
∫
x
⋅
sin
2
x
⋅
cos
5
x
d
x
Show model answer
[QEx 3.3 I (xx) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q118
#118
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
cos
(
x
3
)
d
x
\int \cos \left(\sqrt[3]{x}\right)\, dx
∫
cos
(
3
x
)
d
x
Show model answer
[QEx 3.3 I (xxi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 7 questions
Integrate the following functions w. r. t. x :
Q119
#119
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
2
x
⋅
sin
3
x
d
x
\int e^{2x} \cdot \sin 3x\, dx
∫
e
2
x
⋅
sin
3
x
d
x
Show model answer
[QEx 3.3 II (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q120
#120
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
−
x
⋅
cos
2
x
d
x
\int e^{-x} \cdot \cos 2x\, dx
∫
e
−
x
⋅
cos
2
x
d
x
Show model answer
[QEx 3.3 II (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q121
#121
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
sin
(
log
x
)
d
x
\int \sin (\log x)\, dx
∫
sin
(
lo
g
x
)
d
x
Show model answer
[QEx 3.3 II (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q122
#122
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
5
x
2
+
3
d
x
\int \sqrt{5x^2 + 3}\, dx
∫
5
x
2
+
3
d
x
Show model answer
[QEx 3.3 II (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q123
#123
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
x
2
⋅
a
2
−
x
6
d
x
\int x^2 \cdot \sqrt{a^2 - x^6}\, dx
∫
x
2
⋅
a
2
−
x
6
d
x
Show model answer
[QEx 3.3 II (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q124
#124
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
(
x
−
3
)
(
7
−
x
)
d
x
\int \sqrt{(x - 3)(7 - x)}\, dx
∫
(
x
−
3
)
(
7
−
x
)
d
x
Show model answer
[QEx 3.3 II (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q125
#125
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
4
x
(
4
x
+
4
)
d
x
\int \sqrt{4^x (4^x + 4)}\, dx
∫
4
x
(
4
x
+
4
)
d
x
Show model answer
[QEx 3.3 II (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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