PYQ Vault
Bank
Guides
Notes
Mocks
Board
NDA
Sign in
Filtered questions
314 questions match
Filters
2
Download
· 314
Filtering by:
Exam: CBSE Class 12
Clear all
Copy link
Q26
#26
Mathematics → Integrals → Integration as the Inverse of Differentiation
·
Moderate
Add
If
d
d
x
f
(
x
)
=
4
x
3
−
3
x
4
\dfrac{d}{dx}f(x) = 4x^3 - \dfrac{3}{x^4}
d
x
d
f
(
x
)
=
4
x
3
−
x
4
3
such that
f
(
2
)
=
0
f(2) = 0
f
(
2
)
=
0
. Then
f
(
x
)
f(x)
f
(
x
)
is
A
x
4
+
1
x
3
−
129
8
x^4 + \dfrac{1}{x^3} - \dfrac{129}{8}
x
4
+
x
3
1
−
8
129
B
x
3
+
1
x
4
+
129
8
x^3 + \dfrac{1}{x^4} + \dfrac{129}{8}
x
3
+
x
4
1
+
8
129
C
x
4
+
1
x
3
+
129
8
x^4 + \dfrac{1}{x^3} + \dfrac{129}{8}
x
4
+
x
3
1
+
8
129
D
x
3
+
1
x
4
−
129
8
x^3 + \dfrac{1}{x^4} - \dfrac{129}{8}
x
3
+
x
4
1
−
8
129
Tap an option to check your answer.
[QEx 7.1 Q22 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q27
#27
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
Evaluate
∫
−
1
2
∣
x
3
−
x
∣
d
x
\int_{-1}^{2} |x^3 - x|\,dx
∫
−
1
2
∣
x
3
−
x
∣
d
x
.
Show model answer
[Q7.10 Eg.28 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q28
#28
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
Evaluate
∫
−
π
/
4
π
/
4
sin
2
x
d
x
\int_{-\pi/4}^{\pi/4} \sin^2 x\,dx
∫
−
π
/4
π
/4
sin
2
x
d
x
.
Show model answer
[Q7.10 Eg.29 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q29
#29
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
Evaluate
∫
0
π
x
sin
x
1
+
cos
2
x
d
x
\int_{0}^{\pi} \frac{x \sin x}{1 + \cos^2 x}\,dx
∫
0
π
1
+
c
o
s
2
x
x
s
i
n
x
d
x
.
Show model answer
[Q7.10 Eg.30 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q30
#30
Mathematics → Integrals → Properties of Definite Integrals
·
Easy
Add
Evaluate
∫
−
1
1
sin
5
x
cos
4
x
d
x
\int_{-1}^{1} \sin^5 x \cos^4 x\,dx
∫
−
1
1
sin
5
x
cos
4
x
d
x
.
Show model answer
[Q7.10 Eg.31 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q31
#31
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
Evaluate
∫
0
π
/
2
sin
4
x
sin
4
x
+
cos
4
x
d
x
\int_{0}^{\pi/2} \frac{\sin^4 x}{\sin^4 x + \cos^4 x}\,dx
∫
0
π
/2
s
i
n
4
x
+
c
o
s
4
x
s
i
n
4
x
d
x
.
Show model answer
[Q7.10 Eg.32 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q32
#32
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
Evaluate
∫
π
/
6
π
/
3
d
x
1
+
tan
x
\int_{\pi/6}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}}
∫
π
/6
π
/3
1
+
t
a
n
x
d
x
.
Show model answer
[Q7.10 Eg.33 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q33
#33
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
Evaluate
∫
0
π
/
2
log
sin
x
d
x
\int_{0}^{\pi/2} \log \sin x\,dx
∫
0
π
/2
lo
g
sin
x
d
x
.
Show model answer
[Q7.10 Eg.34 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q34
#34
Mathematics → Integrals → Properties of Definite Integrals
·
Easy
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
2
cos
2
x
d
x
\int_{0}^{\pi/2} \cos^2 x\,dx
∫
0
π
/2
cos
2
x
d
x
.
Show model answer
[QEx 7.10 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q35
#35
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
2
sin
x
sin
x
+
cos
x
d
x
\int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}}\,dx
∫
0
π
/2
s
i
n
x
+
c
o
s
x
s
i
n
x
d
x
.
Show model answer
[QEx 7.10 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q36
#36
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
2
sin
3
/
2
x
sin
3
/
2
x
+
cos
3
/
2
x
d
x
\int_{0}^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x}\,dx
∫
0
π
/2
s
i
n
3/2
x
+
c
o
s
3/2
x
s
i
n
3/2
x
d
x
.
Show model answer
[QEx 7.10 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q37
#37
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
2
cos
5
x
sin
5
x
+
cos
5
x
d
x
\int_{0}^{\pi/2} \frac{\cos^5 x}{\sin^5 x + \cos^5 x}\,dx
∫
0
π
/2
s
i
n
5
x
+
c
o
s
5
x
c
o
s
5
x
d
x
.
Show model answer
[QEx 7.10 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q38
#38
Mathematics → Integrals → Properties of Definite Integrals
·
Easy
Add
By using the properties of definite integrals, evaluate the integral
∫
−
5
5
∣
x
+
2
∣
d
x
\int_{-5}^{5} |x + 2|\,dx
∫
−
5
5
∣
x
+
2∣
d
x
.
Show model answer
[QEx 7.10 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q39
#39
Mathematics → Integrals → Properties of Definite Integrals
·
Easy
Add
By using the properties of definite integrals, evaluate the integral
∫
2
8
∣
x
−
5
∣
d
x
\int_{2}^{8} |x - 5|\,dx
∫
2
8
∣
x
−
5∣
d
x
.
Show model answer
[QEx 7.10 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q40
#40
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
1
x
(
1
−
x
)
n
d
x
\int_{0}^{1} x(1 - x)^n\,dx
∫
0
1
x
(
1
−
x
)
n
d
x
.
Show model answer
[QEx 7.10 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q41
#41
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
4
log
(
1
+
tan
x
)
d
x
\int_{0}^{\pi/4} \log(1 + \tan x)\,dx
∫
0
π
/4
lo
g
(
1
+
tan
x
)
d
x
.
Show model answer
[QEx 7.10 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q42
#42
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
2
x
2
−
x
d
x
\int_{0}^{2} x\sqrt{2 - x}\,dx
∫
0
2
x
2
−
x
d
x
.
Show model answer
[QEx 7.10 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q43
#43
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
2
(
2
log
sin
x
−
log
sin
2
x
)
d
x
\int_{0}^{\pi/2}(2\log \sin x - \log \sin 2x)\,dx
∫
0
π
/2
(
2
lo
g
sin
x
−
lo
g
sin
2
x
)
d
x
.
Show model answer
[QEx 7.10 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q44
#44
Mathematics → Integrals → Properties of Definite Integrals
·
Easy
Add
By using the properties of definite integrals, evaluate the integral
∫
−
π
/
2
π
/
2
sin
2
x
d
x
\int_{-\pi/2}^{\pi/2} \sin^2 x\,dx
∫
−
π
/2
π
/2
sin
2
x
d
x
.
Show model answer
[QEx 7.10 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q45
#45
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
x
d
x
1
+
sin
x
\int_{0}^{\pi} \frac{x\,dx}{1 + \sin x}
∫
0
π
1
+
s
i
n
x
x
d
x
.
Show model answer
[QEx 7.10 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q46
#46
Mathematics → Integrals → Properties of Definite Integrals
·
Easy
Add
By using the properties of definite integrals, evaluate the integral
∫
−
π
/
2
π
/
2
sin
7
x
d
x
\int_{-\pi/2}^{\pi/2} \sin^7 x\,dx
∫
−
π
/2
π
/2
sin
7
x
d
x
.
Show model answer
[QEx 7.10 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q47
#47
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
2
π
cos
5
x
d
x
\int_{0}^{2\pi} \cos^5 x\,dx
∫
0
2
π
cos
5
x
d
x
.
Show model answer
[QEx 7.10 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q48
#48
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
/
2
sin
x
−
cos
x
1
+
sin
x
cos
x
d
x
\int_{0}^{\pi/2} \frac{\sin x - \cos x}{1 + \sin x \cos x}\,dx
∫
0
π
/2
1
+
s
i
n
x
c
o
s
x
s
i
n
x
−
c
o
s
x
d
x
.
Show model answer
[QEx 7.10 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q49
#49
Mathematics → Integrals → Properties of Definite Integrals
·
Hard
Add
By using the properties of definite integrals, evaluate the integral
∫
0
π
log
(
1
+
cos
x
)
d
x
\int_{0}^{\pi} \log(1 + \cos x)\,dx
∫
0
π
lo
g
(
1
+
cos
x
)
d
x
.
Show model answer
[QEx 7.10 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q50
#50
Mathematics → Integrals → Properties of Definite Integrals
·
Moderate
Add
By using the properties of definite integrals, evaluate the integral
∫
0
a
x
x
+
a
−
x
d
x
\int_{0}^{a} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}}\,dx
∫
0
a
x
+
a
−
x
x
d
x
.
Show model answer
[QEx 7.10 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Prev
Page 2 of 13
Next
1
2
3
…
13
PYQ Vault
Bank
Guides
Notes
Mocks
Board
NDA
Sign in