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Exam: CBSE Class 12
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Q126
#126
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
∫
sin
2
x
−
cos
2
x
sin
2
x
cos
2
x
d
x
\displaystyle\int \dfrac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x}\,dx
∫
sin
2
x
cos
2
x
sin
2
x
−
cos
2
x
d
x
is equal to
A
tan
x
+
cot
x
+
C
\tan x + \cot x + C
tan
x
+
cot
x
+
C
B
tan
x
+
csc
x
+
C
\tan x + \csc x + C
tan
x
+
csc
x
+
C
C
−
tan
x
+
cot
x
+
C
-\tan x + \cot x + C
−
tan
x
+
cot
x
+
C
D
tan
x
+
sec
x
+
C
\tan x + \sec x + C
tan
x
+
sec
x
+
C
Tap an option to check your answer.
[QEx 7.3 Q23 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q127
#127
Mathematics → Integrals → Integration using Trigonometric Identities
·
Moderate
Add
∫
e
x
(
1
+
x
)
cos
2
(
e
x
x
)
d
x
\displaystyle\int \dfrac{e^x (1 + x)}{\cos^2 (e^x x)}\,dx
∫
cos
2
(
e
x
x
)
e
x
(
1
+
x
)
d
x
equals
A
−
cot
(
e
x
x
)
+
C
-\cot (e^x x) + C
−
cot
(
e
x
x
)
+
C
B
tan
(
x
e
x
)
+
C
\tan (x e^x) + C
tan
(
x
e
x
)
+
C
C
tan
(
e
x
)
+
C
\tan (e^x) + C
tan
(
e
x
)
+
C
D
cot
(
e
x
)
+
C
\cot (e^x) + C
cot
(
e
x
)
+
C
Tap an option to check your answer.
[QEx 7.3 Q24 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q128
#128
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Find the following integrals: (i)
∫
d
x
x
2
−
16
\int \frac{dx}{x^2-16}
∫
x
2
−
16
d
x
(ii)
∫
d
x
2
x
−
x
2
\int \frac{dx}{\sqrt{2x-x^2}}
∫
2
x
−
x
2
d
x
Show model answer
[Q7.4 Eg.8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q129
#129
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Find the following integrals: (i)
∫
d
x
x
2
−
6
x
+
13
\int \frac{dx}{x^2-6x+13}
∫
x
2
−
6
x
+
13
d
x
(ii)
∫
d
x
3
x
2
+
13
x
−
10
\int \frac{dx}{3x^2+13x-10}
∫
3
x
2
+
13
x
−
10
d
x
(iii)
∫
d
x
5
x
2
−
2
x
\int \frac{dx}{\sqrt{5x^2-2x}}
∫
5
x
2
−
2
x
d
x
Show model answer
[Q7.4 Eg.9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q130
#130
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Find the following integrals: (i)
∫
x
+
2
2
x
2
+
6
x
+
5
d
x
\int \frac{x+2}{2x^2+6x+5}\,dx
∫
2
x
2
+
6
x
+
5
x
+
2
d
x
(ii)
∫
x
+
3
5
−
4
x
−
x
2
d
x
\int \frac{x+3}{\sqrt{5-4x-x^2}}\,dx
∫
5
−
4
x
−
x
2
x
+
3
d
x
Show model answer
[Q7.4 Eg.10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q131
#131
Mathematics → Integrals → Integrals of Some Particular Functions
·
Easy
Add
Integrate
3
x
2
x
6
+
1
\frac{3x^2}{x^6+1}
x
6
+
1
3
x
2
.
Show model answer
[QEx 7.4 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q132
#132
Mathematics → Integrals → Integrals of Some Particular Functions
·
Easy
Add
Integrate
1
1
+
4
x
2
\frac{1}{\sqrt{1+4x^2}}
1
+
4
x
2
1
.
Show model answer
[QEx 7.4 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q133
#133
Mathematics → Integrals → Integrals of Some Particular Functions
·
Easy
Add
Integrate
1
(
2
−
x
)
2
+
1
\frac{1}{\sqrt{(2-x)^2+1}}
(
2
−
x
)
2
+
1
1
.
Show model answer
[QEx 7.4 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q134
#134
Mathematics → Integrals → Integrals of Some Particular Functions
·
Easy
Add
Integrate
1
9
−
25
x
2
\frac{1}{\sqrt{9-25x^2}}
9
−
25
x
2
1
.
Show model answer
[QEx 7.4 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q135
#135
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
3
x
1
+
2
x
4
\frac{3x}{1+2x^4}
1
+
2
x
4
3
x
.
Show model answer
[QEx 7.4 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q136
#136
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
x
2
1
−
x
6
\frac{x^2}{1-x^6}
1
−
x
6
x
2
.
Show model answer
[QEx 7.4 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q137
#137
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
x
−
1
x
2
−
1
\frac{x-1}{\sqrt{x^2-1}}
x
2
−
1
x
−
1
.
Show model answer
[QEx 7.4 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q138
#138
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
x
2
x
6
+
a
6
\frac{x^2}{\sqrt{x^6+a^6}}
x
6
+
a
6
x
2
.
Show model answer
[QEx 7.4 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q139
#139
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
sec
2
x
tan
2
x
+
4
\frac{\sec^2 x}{\sqrt{\tan^2 x+4}}
t
a
n
2
x
+
4
s
e
c
2
x
.
Show model answer
[QEx 7.4 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q140
#140
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
1
x
2
+
2
x
+
2
\frac{1}{\sqrt{x^2+2x+2}}
x
2
+
2
x
+
2
1
.
Show model answer
[QEx 7.4 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q141
#141
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
1
9
x
2
+
6
x
+
5
\frac{1}{9x^2+6x+5}
9
x
2
+
6
x
+
5
1
.
Show model answer
[QEx 7.4 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q142
#142
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
1
7
−
6
x
−
x
2
\frac{1}{\sqrt{7-6x-x^2}}
7
−
6
x
−
x
2
1
.
Show model answer
[QEx 7.4 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q143
#143
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
1
(
x
−
1
)
(
x
−
2
)
\frac{1}{\sqrt{(x-1)(x-2)}}
(
x
−
1
)
(
x
−
2
)
1
.
Show model answer
[QEx 7.4 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q144
#144
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
1
8
+
3
x
−
x
2
\frac{1}{\sqrt{8+3x-x^2}}
8
+
3
x
−
x
2
1
.
Show model answer
[QEx 7.4 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q145
#145
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
Integrate
1
(
x
−
a
)
(
x
−
b
)
\frac{1}{\sqrt{(x-a)(x-b)}}
(
x
−
a
)
(
x
−
b
)
1
.
Show model answer
[QEx 7.4 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q146
#146
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
4
x
+
1
2
x
2
+
x
−
3
\frac{4x+1}{\sqrt{2x^2+x-3}}
2
x
2
+
x
−
3
4
x
+
1
.
Show model answer
[QEx 7.4 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q147
#147
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
x
+
2
x
2
−
1
\frac{x+2}{\sqrt{x^2-1}}
x
2
−
1
x
+
2
.
Show model answer
[QEx 7.4 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q148
#148
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
5
x
−
2
1
+
2
x
+
3
x
2
\frac{5x-2}{1+2x+3x^2}
1
+
2
x
+
3
x
2
5
x
−
2
.
Show model answer
[QEx 7.4 Q18 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q149
#149
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
6
x
+
7
(
x
−
5
)
(
x
−
4
)
\frac{6x+7}{\sqrt{(x-5)(x-4)}}
(
x
−
5
)
(
x
−
4
)
6
x
+
7
.
Show model answer
[QEx 7.4 Q19 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q150
#150
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
x
+
2
4
x
−
x
2
\frac{x+2}{\sqrt{4x-x^2}}
4
x
−
x
2
x
+
2
.
Show model answer
[QEx 7.4 Q20 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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