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Exam: CBSE Class 12
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Q201
#201
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
(
sin
−
1
x
)
2
(\sin^{-1} x)^{2}
(
sin
−
1
x
)
2
.
Show model answer
[QEx 7.6 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q202
#202
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
x
cos
−
1
x
1
−
x
2
\dfrac{x \cos^{-1} x}{\sqrt{1-x^{2}}}
1
−
x
2
x
cos
−
1
x
.
Show model answer
[QEx 7.6 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q203
#203
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
Integrate the function
x
sec
2
x
x \sec^{2} x
x
sec
2
x
.
Show model answer
[QEx 7.6 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q204
#204
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
Integrate the function
tan
−
1
x
\tan^{-1} x
tan
−
1
x
.
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[QEx 7.6 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q205
#205
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
x
(
log
x
)
2
x (\log x)^{2}
x
(
lo
g
x
)
2
.
Show model answer
[QEx 7.6 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q206
#206
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
Integrate the function
(
x
2
+
1
)
log
x
(x^{2}+1) \log x
(
x
2
+
1
)
lo
g
x
.
Show model answer
[QEx 7.6 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q207
#207
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
Integrate the function
e
x
(
sin
x
+
cos
x
)
e^{x} (\sin x + \cos x)
e
x
(
sin
x
+
cos
x
)
.
Show model answer
[QEx 7.6 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q208
#208
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
Integrate the function
x
e
x
(
1
+
x
)
2
\dfrac{x\, e^{x}}{(1+x)^{2}}
(
1
+
x
)
2
x
e
x
.
Show model answer
[QEx 7.6 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q209
#209
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
e
x
(
1
+
sin
x
1
+
cos
x
)
e^{x}\left(\dfrac{1+\sin x}{1+\cos x}\right)
e
x
(
1
+
cos
x
1
+
sin
x
)
.
Show model answer
[QEx 7.6 Q18 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q210
#210
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
Integrate the function
e
x
(
1
x
−
1
x
2
)
e^{x}\left(\dfrac{1}{x} - \dfrac{1}{x^{2}}\right)
e
x
(
x
1
−
x
2
1
)
.
Show model answer
[QEx 7.6 Q19 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q211
#211
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
(
x
−
3
)
e
x
(
x
−
1
)
3
\dfrac{(x-3)\, e^{x}}{(x-1)^{3}}
(
x
−
1
)
3
(
x
−
3
)
e
x
.
Show model answer
[QEx 7.6 Q20 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q212
#212
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
e
2
x
sin
x
e^{2x} \sin x
e
2
x
sin
x
.
Show model answer
[QEx 7.6 Q21 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q213
#213
Mathematics → Integrals → Integration by Parts
·
Hard
Add
Integrate the function
sin
−
1
(
2
x
1
+
x
2
)
\sin^{-1}\left(\dfrac{2x}{1+x^{2}}\right)
sin
−
1
(
1
+
x
2
2
x
)
.
Show model answer
[QEx 7.6 Q22 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q214
#214
Mathematics → Integrals → Integration by Parts
·
Easy
Add
∫
x
2
e
x
3
d
x
\int x^{2} e^{x^{3}} \, dx
∫
x
2
e
x
3
d
x
equals
A
1
3
e
x
3
+
C
\frac{1}{3} e^{x^{3}} + C
3
1
e
x
3
+
C
B
1
3
e
x
2
+
C
\frac{1}{3} e^{x^{2}} + C
3
1
e
x
2
+
C
C
1
2
e
x
3
+
C
\frac{1}{2} e^{x^{3}} + C
2
1
e
x
3
+
C
D
1
2
e
x
2
+
C
\frac{1}{2} e^{x^{2}} + C
2
1
e
x
2
+
C
Tap an option to check your answer.
[QEx 7.6 Q23 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q215
#215
Mathematics → Integrals → Integration by Parts
·
Moderate
Add
∫
e
x
sec
x
(
1
+
tan
x
)
d
x
\int e^{x} \sec x\, (1 + \tan x) \, dx
∫
e
x
sec
x
(
1
+
tan
x
)
d
x
equals
A
e
x
cos
x
+
C
e^{x} \cos x + C
e
x
cos
x
+
C
B
e
x
sec
x
+
C
e^{x} \sec x + C
e
x
sec
x
+
C
C
e
x
sin
x
+
C
e^{x} \sin x + C
e
x
sin
x
+
C
D
e
x
tan
x
+
C
e^{x} \tan x + C
e
x
tan
x
+
C
Tap an option to check your answer.
[QEx 7.6 Q24 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q216
#216
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Find
∫
x
2
+
2
x
+
5
d
x
\int \sqrt{x^2 + 2x + 5}\,dx
∫
x
2
+
2
x
+
5
d
x
.
Show model answer
[Q7.7 Eg.23 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q217
#217
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Find
∫
3
−
2
x
−
x
2
d
x
\int \sqrt{3 - 2x - x^2}\,dx
∫
3
−
2
x
−
x
2
d
x
.
Show model answer
[Q7.7 Eg.24 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q218
#218
Mathematics → Integrals → Integrals of Special Forms
·
Easy
Add
Integrate the function
4
−
x
2
\sqrt{4 - x^2}
4
−
x
2
.
Show model answer
[QEx 7.7 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q219
#219
Mathematics → Integrals → Integrals of Special Forms
·
Easy
Add
Integrate the function
1
−
4
x
2
\sqrt{1 - 4x^2}
1
−
4
x
2
.
Show model answer
[QEx 7.7 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q220
#220
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Integrate the function
x
2
+
4
x
+
6
\sqrt{x^2 + 4x + 6}
x
2
+
4
x
+
6
.
Show model answer
[QEx 7.7 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q221
#221
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Integrate the function
x
2
+
4
x
+
1
\sqrt{x^2 + 4x + 1}
x
2
+
4
x
+
1
.
Show model answer
[QEx 7.7 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q222
#222
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Integrate the function
1
−
4
x
−
x
2
\sqrt{1 - 4x - x^2}
1
−
4
x
−
x
2
.
Show model answer
[QEx 7.7 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q223
#223
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Integrate the function
x
2
+
4
x
−
5
\sqrt{x^2 + 4x - 5}
x
2
+
4
x
−
5
.
Show model answer
[QEx 7.7 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q224
#224
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Integrate the function
1
+
3
x
−
x
2
\sqrt{1 + 3x - x^2}
1
+
3
x
−
x
2
.
Show model answer
[QEx 7.7 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q225
#225
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
Integrate the function
x
2
+
3
x
\sqrt{x^2 + 3x}
x
2
+
3
x
.
Show model answer
[QEx 7.7 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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