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Exam: Maharashtra HSC Class 12
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Set · 1 question
Integrate the following functions w. r. t. x :
Q51
#51
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
1
x
⋅
log
x
⋅
log
(
log
x
)
d
x
\int \frac{1}{x \cdot \log x \cdot \log (\log x)}\, dx
∫
x
⋅
l
o
g
x
⋅
l
o
g
(
l
o
g
x
)
1
d
x
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[QEx 3.2(A) I (25) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 17 questions
Integrate the following functions w. r. t. x :
Q52
#52
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
cos
3
x
−
cos
4
x
sin
3
x
+
sin
4
x
d
x
\int \frac{\cos 3x - \cos 4x}{\sin 3x + \sin 4x}\, dx
∫
s
i
n
3
x
+
s
i
n
4
x
c
o
s
3
x
−
c
o
s
4
x
d
x
Show model answer
[QEx 3.2(A) II (1) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q53
#53
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
cos
x
sin
(
x
−
a
)
d
x
\int \frac{\cos x}{\sin (x - a)}\, dx
∫
s
i
n
(
x
−
a
)
c
o
s
x
d
x
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[QEx 3.2(A) II (2) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q54
#54
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
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
[QEx 3.2(A) II (3) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q55
#55
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
sin
x
⋅
cos
x
+
2
cos
2
x
d
x
\int \frac{1}{\sin x \cdot \cos x + 2 \cos^2 x}\, dx
∫
s
i
n
x
⋅
c
o
s
x
+
2
c
o
s
2
x
1
d
x
Show model answer
[QEx 3.2(A) II (4) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q56
#56
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
sin
x
+
2
cos
x
3
sin
x
+
4
cos
x
d
x
\int \frac{\sin x + 2 \cos x}{3 \sin x + 4 \cos x}\, dx
∫
3
s
i
n
x
+
4
c
o
s
x
s
i
n
x
+
2
c
o
s
x
d
x
Show model answer
[QEx 3.2(A) II (5) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q57
#57
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
1
2
+
3
tan
x
d
x
\int \frac{1}{2 + 3 \tan x}\, dx
∫
2
+
3
t
a
n
x
1
d
x
Show model answer
[QEx 3.2(A) II (6) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q58
#58
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
4
e
x
−
25
2
e
x
−
5
d
x
\int \frac{4 e^x - 25}{2 e^x - 5}\, dx
∫
2
e
x
−
5
4
e
x
−
25
d
x
Show model answer
[QEx 3.2(A) II (7) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q59
#59
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
20
+
12
e
x
3
e
x
+
4
d
x
\int \frac{20 + 12 e^x}{3 e^x + 4}\, dx
∫
3
e
x
+
4
20
+
12
e
x
d
x
Show model answer
[QEx 3.2(A) II (8) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q60
#60
Mathematics → Indefinite Integration → Integration by Substitution
·
Moderate
Add
∫
3
e
2
x
+
5
4
e
2
x
−
5
d
x
\int \frac{3 e^{2x} + 5}{4 e^{2x} - 5}\, dx
∫
4
e
2
x
−
5
3
e
2
x
+
5
d
x
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[QEx 3.2(A) II (9) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q61
#61
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
cos
8
x
⋅
cot
x
d
x
\int \cos^8 x \cdot \cot x\, dx
∫
cos
8
x
⋅
cot
x
d
x
Show model answer
[QEx 3.2(A) II (10) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q62
#62
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
tan
5
x
d
x
\int \tan^5 x\, dx
∫
tan
5
x
d
x
Show model answer
[QEx 3.2(A) II (11) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q63
#63
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
cos
7
x
d
x
\int \cos^7 x\, dx
∫
cos
7
x
d
x
Show model answer
[QEx 3.2(A) II (12) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q64
#64
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
tan
3
x
⋅
tan
2
x
⋅
tan
x
d
x
\int \tan 3x \cdot \tan 2x \cdot \tan x\, dx
∫
tan
3
x
⋅
tan
2
x
⋅
tan
x
d
x
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[QEx 3.2(A) II (13) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q65
#65
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
sin
5
x
⋅
cos
8
x
d
x
\int \sin^5 x \cdot \cos^8 x\, dx
∫
sin
5
x
⋅
cos
8
x
d
x
Show model answer
[QEx 3.2(A) II (14) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q66
#66
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
3
cos
2
x
⋅
sin
2
x
d
x
\int 3^{\cos^2 x} \cdot \sin 2x\, dx
∫
3
c
o
s
2
x
⋅
sin
2
x
d
x
Show model answer
[QEx 3.2(A) II (15) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q67
#67
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
sin
6
x
sin
10
x
⋅
sin
4
x
d
x
\int \frac{\sin 6x}{\sin 10x \cdot \sin 4x}\, dx
∫
s
i
n
10
x
⋅
s
i
n
4
x
s
i
n
6
x
d
x
Show model answer
[QEx 3.2(A) II (16) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q68
#68
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
sin
x
⋅
cos
3
x
1
+
cos
2
x
d
x
\int \frac{\sin x \cdot \cos^3 x}{1 + \cos^2 x}\, dx
∫
1
+
c
o
s
2
x
s
i
n
x
⋅
c
o
s
3
x
d
x
Show model answer
[QEx 3.2(A) II (17) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 7 questions
Evaluate the following :
Q69
#69
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Easy
Add
∫
1
4
x
2
−
3
d
x
\int \frac{1}{4x^2 - 3} \, dx
∫
4
x
2
−
3
1
d
x
Show model answer
[QEx 3.2(B) I (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q70
#70
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Easy
Add
∫
1
25
−
9
x
2
d
x
\int \frac{1}{25 - 9x^2} \, dx
∫
25
−
9
x
2
1
d
x
Show model answer
[QEx 3.2(B) I (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q71
#71
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Easy
Add
∫
1
7
+
2
x
2
d
x
\int \frac{1}{7 + 2x^2} \, dx
∫
7
+
2
x
2
1
d
x
Show model answer
[QEx 3.2(B) I (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q72
#72
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Easy
Add
∫
1
3
x
2
+
8
d
x
\int \frac{1}{\sqrt{3x^2 + 8}} \, dx
∫
3
x
2
+
8
1
d
x
Show model answer
[QEx 3.2(B) I (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q73
#73
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Easy
Add
∫
1
11
−
4
x
2
d
x
\int \frac{1}{\sqrt{11 - 4x^2}} \, dx
∫
11
−
4
x
2
1
d
x
Show model answer
[QEx 3.2(B) I (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q74
#74
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Easy
Add
∫
1
2
x
2
−
5
d
x
\int \frac{1}{\sqrt{2x^2 - 5}} \, dx
∫
2
x
2
−
5
1
d
x
Show model answer
[QEx 3.2(B) I (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q75
#75
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
9
+
x
9
−
x
d
x
\int \sqrt{\frac{9 + x}{9 - x}} \, dx
∫
9
−
x
9
+
x
d
x
Show model answer
[QEx 3.2(B) I (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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