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Exam: Maharashtra HSC Class 12
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Set · 5 questions
Integrate the following functions w. r. t. x :
Q1
#1
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
∫
(
x
3
+
x
2
−
x
+
1
)
d
x
\int (x^3 + x^2 - x + 1)\, dx
∫
(
x
3
+
x
2
−
x
+
1
)
d
x
Show model answer
[QEx 3.1 I (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q2
#2
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
∫
x
2
(
1
−
2
x
)
2
d
x
\int x^2 \left(1 - \dfrac{2}{x}\right)^2 dx
∫
x
2
(
1
−
x
2
)
2
d
x
Show model answer
[QEx 3.1 I (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q3
#3
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
∫
(
3
sec
2
x
−
4
x
+
1
x
x
−
7
)
d
x
\int \left(3 \sec^2 x - \dfrac{4}{x} + \dfrac{1}{x\sqrt{x}} - 7\right) dx
∫
(
3
sec
2
x
−
x
4
+
x
x
1
−
7
)
d
x
Show model answer
[QEx 3.1 I (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q4
#4
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
∫
(
2
x
3
−
5
x
+
3
x
+
4
x
5
)
d
x
\int \left(2x^3 - 5x + \dfrac{3}{x} + \dfrac{4}{x^5}\right) dx
∫
(
2
x
3
−
5
x
+
x
3
+
x
5
4
)
d
x
Show model answer
[QEx 3.1 I (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q5
#5
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
3
x
3
−
2
x
+
5
x
x
d
x
\int \dfrac{3x^3 - 2x + 5}{x\sqrt{x}}\, dx
∫
x
x
3
x
3
−
2
x
+
5
d
x
Show model answer
[QEx 3.1 I (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 10 questions
Evaluate :
Q6
#6
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
∫
tan
2
x
d
x
\int \tan^2 x\, dx
∫
tan
2
x
d
x
Show model answer
[QEx 3.1 II (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q7
#7
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
sin
2
x
cos
x
d
x
\int \dfrac{\sin 2x}{\cos x}\, dx
∫
cos
x
sin
2
x
d
x
Show model answer
[QEx 3.1 II (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q8
#8
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
sin
x
cos
2
x
d
x
\int \dfrac{\sin x}{\cos^2 x}\, dx
∫
cos
2
x
sin
x
d
x
Show model answer
[QEx 3.1 II (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q9
#9
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
cos
2
x
sin
2
x
d
x
\int \dfrac{\cos 2x}{\sin^2 x}\, dx
∫
sin
2
x
cos
2
x
d
x
Show model answer
[QEx 3.1 II (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q10
#10
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
cos
2
x
sin
2
x
⋅
cos
2
x
d
x
\int \dfrac{\cos 2x}{\sin^2 x \cdot \cos^2 x}\, dx
∫
sin
2
x
⋅
cos
2
x
cos
2
x
d
x
Show model answer
[QEx 3.1 II (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q11
#11
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
sin
x
1
+
sin
x
d
x
\int \dfrac{\sin x}{1 + \sin x}\, dx
∫
1
+
sin
x
sin
x
d
x
Show model answer
[QEx 3.1 II (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q12
#12
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
tan
x
sec
x
+
tan
x
d
x
\int \dfrac{\tan x}{\sec x + \tan x}\, dx
∫
sec
x
+
tan
x
tan
x
d
x
Show model answer
[QEx 3.1 II (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q13
#13
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
1
+
sin
2
x
d
x
\int \sqrt{1 + \sin 2x}\, dx
∫
1
+
sin
2
x
d
x
Show model answer
[QEx 3.1 II (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q14
#14
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
1
−
cos
2
x
d
x
\int \sqrt{1 - \cos 2x}\, dx
∫
1
−
cos
2
x
d
x
Show model answer
[QEx 3.1 II (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q15
#15
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
sin
4
x
⋅
cos
3
x
d
x
\int \sin 4x \cdot \cos 3x\, dx
∫
sin
4
x
⋅
cos
3
x
d
x
Show model answer
[QEx 3.1 II (x) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 10 questions
Evaluate :
Q16
#16
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
x
x
+
2
d
x
\int \dfrac{x}{x + 2}\, dx
∫
x
+
2
x
d
x
Show model answer
[QEx 3.1 III (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q17
#17
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
4
x
+
3
2
x
+
1
d
x
\int \dfrac{4x + 3}{2x + 1}\, dx
∫
2
x
+
1
4
x
+
3
d
x
Show model answer
[QEx 3.1 III (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q18
#18
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
5
x
+
2
3
x
−
4
d
x
\int \dfrac{5x + 2}{3x - 4}\, dx
∫
3
x
−
4
5
x
+
2
d
x
Show model answer
[QEx 3.1 III (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q19
#19
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
x
−
2
x
+
5
d
x
\int \dfrac{x - 2}{\sqrt{x + 5}}\, dx
∫
x
+
5
x
−
2
d
x
Show model answer
[QEx 3.1 III (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q20
#20
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
2
x
−
7
4
x
−
1
d
x
\int \dfrac{2x - 7}{\sqrt{4x - 1}}\, dx
∫
4
x
−
1
2
x
−
7
d
x
Show model answer
[QEx 3.1 III (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q21
#21
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
sin
4
x
cos
2
x
d
x
\int \dfrac{\sin 4x}{\cos 2x}\, dx
∫
cos
2
x
sin
4
x
d
x
Show model answer
[QEx 3.1 III (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q22
#22
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Moderate
Add
∫
1
+
sin
5
x
d
x
\int \sqrt{1 + \sin 5x}\, dx
∫
1
+
sin
5
x
d
x
Show model answer
[QEx 3.1 III (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q23
#23
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Easy
Add
∫
cos
2
x
d
x
\int \cos^2 x\, dx
∫
cos
2
x
d
x
Show model answer
[QEx 3.1 III (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q24
#24
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
∫
2
x
−
x
+
3
d
x
\int \dfrac{2}{\sqrt{x} - \sqrt{x + 3}}\, dx
∫
x
−
x
+
3
2
d
x
Show model answer
[QEx 3.1 III (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q25
#25
Mathematics → Indefinite Integration → Elementary Integration and Standard Formulae
·
Hard
Add
∫
3
7
x
−
2
−
7
x
−
5
d
x
\int \dfrac{3}{\sqrt{7x - 2} - \sqrt{7x - 5}}\, dx
∫
7
x
−
2
−
7
x
−
5
3
d
x
Show model answer
[QEx 3.1 III (x) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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