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Exam: Maharashtra HSC Class 12
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Q201
#201
Mathematics → Indefinite Integration → Integration by Substitution
·
Hard
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Integrate:
1
x
3
⋅
x
2
−
1
\ \dfrac{1}{x^3\cdot\sqrt{x^2-1}}
x
3
⋅
x
2
−
1
1
Show model answer
[QMisc III Q.10 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q202
#202
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Hard
Add
Integrate:
3
x
+
1
−
2
x
2
+
x
+
3
\ \dfrac{3x+1}{\sqrt{-2x^2+x+3}}
−
2
x
2
+
x
+
3
3
x
+
1
Show model answer
[QMisc III Q.11 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q203
#203
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
Integrate:
log
(
x
2
+
1
)
\ \log(x^2+1)
lo
g
(
x
2
+
1
)
Show model answer
[QMisc III Q.12 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q204
#204
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
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Integrate:
e
2
x
⋅
sin
x
⋅
cos
x
\ e^{2x}\cdot\sin x\cdot\cos x
e
2
x
⋅
sin
x
⋅
cos
x
Show model answer
[QMisc III Q.13 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q205
#205
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
Integrate:
x
2
(
x
−
1
)
(
3
x
−
1
)
(
3
x
−
2
)
\ \dfrac{x^2}{(x-1)(3x-1)(3x-2)}
(
x
−
1
)
(
3
x
−
1
)
(
3
x
−
2
)
x
2
Show model answer
[QMisc III Q.14 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q206
#206
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
Integrate:
1
sin
x
+
sin
2
x
\ \dfrac{1}{\sin x+\sin 2x}
sin
x
+
sin
2
x
1
Show model answer
[QMisc III Q.15 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q207
#207
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
Integrate:
sec
2
x
⋅
7
+
2
tan
x
−
tan
2
x
\ \sec^2 x\cdot\sqrt{7+2\tan x-\tan^2 x}
sec
2
x
⋅
7
+
2
tan
x
−
tan
2
x
Show model answer
[QMisc III Q.16 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q208
#208
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
Integrate:
x
+
5
x
3
+
3
x
2
−
x
−
3
\ \dfrac{x+5}{x^3+3x^2-x-3}
x
3
+
3
x
2
−
x
−
3
x
+
5
Show model answer
[QMisc III Q.17 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q209
#209
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
Integrate:
1
x
⋅
(
x
5
+
1
)
\ \dfrac{1}{x\cdot(x^5+1)}
x
⋅
(
x
5
+
1
)
1
Show model answer
[QMisc III Q.18 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q210
#210
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
Integrate:
tan
x
sin
x
⋅
cos
x
\ \dfrac{\sqrt{\tan x}}{\sin x\cdot\cos x}
sin
x
⋅
cos
x
tan
x
Show model answer
[QMisc III Q.19 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q211
#211
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
Integrate:
sec
4
x
⋅
csc
2
x
\ \sec^4 x\cdot\csc^2 x
sec
4
x
⋅
csc
2
x
Show model answer
[QMisc III Q.20 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q212
#212
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
Evaluate:
∫
(
x
3
+
3
x
)
d
x
\int (x^3 + 3^x)\, dx
∫
(
x
3
+
3
x
)
d
x
Show model answer
[Q3.1 SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q213
#213
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
(
sin
x
+
1
x
+
1
x
3
)
d
x
\int \left( \sin x + \dfrac{1}{x} + \dfrac{1}{\sqrt[3]{x}} \right) dx
∫
(
sin
x
+
x
1
+
3
x
1
)
d
x
Show model answer
[Q3.1 SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q214
#214
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
(
tan
x
+
cot
x
)
2
d
x
\int (\tan x + \cot x)^2\, dx
∫
(
tan
x
+
cot
x
)
2
d
x
Show model answer
[Q3.1 SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q215
#215
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
x
+
1
x
+
x
d
x
\int \dfrac{\sqrt{x} + 1}{x + \sqrt{x}}\, dx
∫
x
+
x
x
+
1
d
x
Show model answer
[Q3.1 SolvedEx.4 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q216
#216
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
e
4
log
x
−
e
5
log
x
x
5
d
x
\int \dfrac{e^{4 \log x} - e^{5 \log x}}{x^5}\, dx
∫
x
5
e
4
l
o
g
x
−
e
5
l
o
g
x
d
x
Show model answer
[Q3.1 SolvedEx.5 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q217
#217
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
2
x
+
3
5
x
−
1
d
x
\int \dfrac{2x + 3}{5x - 1}\, dx
∫
5
x
−
1
2
x
+
3
d
x
Show model answer
[Q3.1 SolvedEx.6 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q218
#218
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
Evaluate:
∫
1
3
x
+
1
−
3
x
−
5
d
x
\int \dfrac{1}{\sqrt{3x + 1} - \sqrt{3x - 5}}\, dx
∫
3
x
+
1
−
3
x
−
5
1
d
x
Show model answer
[Q3.1 SolvedEx.7 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q219
#219
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
Evaluate:
∫
2
x
−
7
3
x
−
2
d
x
\int \dfrac{2x - 7}{\sqrt{3x - 2}}\, dx
∫
3
x
−
2
2
x
−
7
d
x
Show model answer
[Q3.1 SolvedEx.8 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q220
#220
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
x
3
x
−
1
d
x
\int \dfrac{x^3}{x - 1}\, dx
∫
x
−
1
x
3
d
x
Show model answer
[Q3.1 SolvedEx.9 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q221
#221
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
3
x
−
4
x
5
x
d
x
\int \dfrac{3^x - 4^x}{5^x}\, dx
∫
5
x
3
x
−
4
x
d
x
Show model answer
[Q3.1 SolvedEx.10 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q222
#222
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
cos
3
x
d
x
\int \cos^3 x\, dx
∫
cos
3
x
d
x
Show model answer
[Q3.1 SolvedEx.11 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q223
#223
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
Evaluate:
∫
1
+
sin
3
x
d
x
\int \sqrt{1 + \sin 3x}\, dx
∫
1
+
sin
3
x
d
x
Show model answer
[Q3.1 SolvedEx.12 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q224
#224
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
Evaluate:
∫
sin
4
x
d
x
\int \sin^4 x\, dx
∫
sin
4
x
d
x
Show model answer
[Q3.1 SolvedEx.13 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q225
#225
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
sin
5
x
⋅
cos
7
x
d
x
\int \sin 5x \cdot \cos 7x\, dx
∫
sin
5
x
⋅
cos
7
x
d
x
Show model answer
[Q3.1 SolvedEx.14 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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