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Exam: Maharashtra HSC Class 12
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Q226
#226
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
sin
3
x
−
cos
3
x
sin
2
x
⋅
cos
2
x
d
x
\int \dfrac{\sin^3 x - \cos^3 x}{\sin^2 x \cdot \cos^2 x}\, dx
∫
sin
2
x
⋅
cos
2
x
sin
3
x
−
cos
3
x
d
x
Show model answer
[Q3.1 SolvedEx.15 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q227
#227
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
1
1
−
sin
x
d
x
\int \dfrac{1}{1 - \sin x}\, dx
∫
1
−
sin
x
1
d
x
Show model answer
[Q3.1 SolvedEx.16 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q228
#228
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
(
cos
x
1
−
cos
x
)
d
x
\int \left( \dfrac{\cos x}{1 - \cos x} \right) dx
∫
(
1
−
cos
x
cos
x
)
d
x
Show model answer
[Q3.1 SolvedEx.17 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q229
#229
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
cos
x
−
cos
2
x
1
−
cos
x
d
x
\int \dfrac{\cos x - \cos 2x}{1 - \cos x}\, dx
∫
1
−
cos
x
cos
x
−
cos
2
x
d
x
Show model answer
[Q3.1 SolvedEx.18 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q230
#230
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
sin
−
1
(
cos
3
x
)
d
x
\int \sin^{-1}(\cos 3x)\, dx
∫
sin
−
1
(
cos
3
x
)
d
x
Show model answer
[Q3.1 SolvedEx.19 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q231
#231
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
Evaluate:
∫
tan
−
1
(
sin
2
x
1
+
cos
2
x
)
d
x
\int \tan^{-1}\left( \dfrac{\sin 2x}{1 + \cos 2x} \right) dx
∫
tan
−
1
(
1
+
cos
2
x
sin
2
x
)
d
x
Show model answer
[Q3.1 SolvedEx.20 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q232
#232
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
Evaluate:
∫
tan
−
1
1
−
sin
x
1
+
sin
x
d
x
\int \tan^{-1} \sqrt{\dfrac{1 - \sin x}{1 + \sin x}}\, dx
∫
tan
−
1
1
+
sin
x
1
−
sin
x
d
x
Show model answer
[Q3.1 SolvedEx.21 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q233
#233
Mathematics → Indefinite Integration → Integration by Substitution
·
Easy
Add
∫
cot
(
log
x
)
x
d
x
\int \frac{\cot (\log x)}{x}\, dx
∫
x
c
o
t
(
l
o
g
x
)
d
x
Show model answer
[Q3.2A SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q234
#234
Mathematics → Indefinite Integration → Integration by Substitution
·
Easy
Add
∫
cos
x
x
d
x
\int \frac{\cos \sqrt{x}}{\sqrt{x}}\, dx
∫
x
c
o
s
x
d
x
Show model answer
[Q3.2A SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q235
#235
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
sec
8
x
cosec
x
d
x
\int \frac{\sec^8 x}{\operatorname{cosec} x}\, dx
∫
cosec
x
s
e
c
8
x
d
x
Show model answer
[Q3.2A SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q236
#236
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
1
x
+
x
d
x
\int \frac{1}{x + \sqrt{x}}\, dx
∫
x
+
x
1
d
x
Show model answer
[Q3.2A SolvedEx.4 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q237
#237
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
5
5
x
⋅
5
x
d
x
\int 5^{5^x} \cdot 5^x\, dx
∫
5
5
x
⋅
5
x
d
x
Show model answer
[Q3.2A SolvedEx.5 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q238
#238
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
1
1
+
e
−
x
d
x
\int \frac{1}{1 + e^{-x}}\, dx
∫
1
+
e
−
x
1
d
x
Show model answer
[Q3.2A SolvedEx.6 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q239
#239
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
e
x
(
1
+
x
)
cos
(
x
⋅
e
x
)
d
x
\int \frac{e^x (1 + x)}{\cos (x \cdot e^x)}\, dx
∫
c
o
s
(
x
⋅
e
x
)
e
x
(
1
+
x
)
d
x
Show model answer
[Q3.2A SolvedEx.7 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q240
#240
Mathematics → Indefinite Integration → Integration by Substitution
·
Hard
Add
∫
1
3
x
+
7
x
−
n
d
x
\int \frac{1}{3x + 7x^{-n}}\, dx
∫
3
x
+
7
x
−
n
1
d
x
Show model answer
[Q3.2A SolvedEx.8 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q241
#241
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
(
3
x
+
2
)
x
−
4
d
x
\int (3x + 2)\, \sqrt{x - 4}\, dx
∫
(
3
x
+
2
)
x
−
4
d
x
Show model answer
[Q3.2A SolvedEx.9 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q242
#242
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
sin
(
x
+
a
)
cos
(
x
−
b
)
d
x
\int \frac{\sin (x + a)}{\cos (x - b)}\, dx
∫
c
o
s
(
x
−
b
)
s
i
n
(
x
+
a
)
d
x
Show model answer
[Q3.2A SolvedEx.10 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q243
#243
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
e
x
+
1
e
x
−
1
d
x
\int \frac{e^x + 1}{e^x - 1}\, dx
∫
e
x
−
1
e
x
+
1
d
x
Show model answer
[Q3.2A SolvedEx.11 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q244
#244
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
1
1
−
tan
x
d
x
\int \frac{1}{1 - \tan x}\, dx
∫
1
−
t
a
n
x
1
d
x
Show model answer
[Q3.2A SolvedEx.12 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q245
#245
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
4
x
2
+
11
d
x
\int \frac{1}{4x^2 + 11}\, dx
∫
4
x
2
+
11
1
d
x
Show model answer
[Q3.2B SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q246
#246
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
a
2
−
b
2
x
2
d
x
\int \frac{1}{a^2 - b^2 x^2}\, dx
∫
a
2
−
b
2
x
2
1
d
x
Show model answer
[Q3.2B SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q247
#247
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
3
x
2
−
7
d
x
\int \frac{1}{\sqrt{3x^2 - 7}}\, dx
∫
3
x
2
−
7
1
d
x
Show model answer
[Q3.2B SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q248
#248
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
x
2
+
8
x
+
12
d
x
\int \frac{1}{x^2 + 8x + 12}\, dx
∫
x
2
+
8
x
+
12
1
d
x
Show model answer
[Q3.2B SolvedEx.4 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q249
#249
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
3
x
2
−
4
x
+
2
d
x
\int \frac{1}{\sqrt{3x^2 - 4x + 2}}\, dx
∫
3
x
2
−
4
x
+
2
1
d
x
Show model answer
[Q3.2B SolvedEx.5 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q250
#250
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
3
−
10
x
−
25
x
2
d
x
\int \frac{1}{3 - 10x - 25x^2}\, dx
∫
3
−
10
x
−
25
x
2
1
d
x
Show model answer
[Q3.2B SolvedEx.6 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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