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Integrals
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Integrals
TEST : 5
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q1.
∫
cos
x
(
1
+
sin
x
)
(
2
+
sin
x
)
d
x
=
A.
log
(
2
−
sin
x
1
−
sin
x
)
+
C
B.
log (1-sin x).(2-sin x) + C
C.
log
(
2
+
sin
x
1
−
sin
2
x
)
+
C
D.
log
(
1
+
sin
x
2
+
sin
x
)
+
C
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q2.
∫
e
x
(
f
(
x
)
+
f
′
(
x
)
)
is equal to
A.
e
x
+
f
(
x
)
+
C
B.
e
f
(
x
)
+
f
(
e
x
)
+
C
C.
e
x
(
f
(
x
)
−
f
′
(
x
)
)
+
C
D.
e
x
f
(
x
)
+
C
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q3.
∫ |x| dx
A.
−
2
x
2
3
+
C
B.
1
C.
(
1
2
)
x
|
x
|
+
C
D.
x
2
2
+ C
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q4.
∫
(
sin
(
log
x
)
+
cos
(
log
x
)
)
dx is equal to
A.
sin (log x) – cos (log x) + C
B.
x sin (log x) +C
C.
log (sinx − cosx) + c
D.
x cos (log x) + C
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q5.
∫
tan
−
1
x
dx is equal to
A.
2
x
tan
−
1
x
+
log
(
1
−
x
2
)
+
C
B.
x
tan
−
1
x -
1
2
log
(
1
+
x
2
)
+
C
C.
x
tan
−
1
x
+
log
(
1
+
x
2
)
+
C
D.
x
tan
−
1
x
+
1
2
log
(
1
+
x
2
)
+
C
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q6.
∫
a
b
log
x
x
d
x
is equal to
A.
log ((b-a)/b-a)
B.
log
(
a
b
)
.
l
o
g
(
b
a
)
C.
log (a+b).log (b–a)
D.
1/2
log
(
a
b
)
.
l
o
g
(
b
a
)
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q7.
If
∫
−
2
5
f
(
x
)
d
x
=
4
,
∫
0
5
(
1
+
f
(
x
)
)
d
x
=
7
,
then the value of the integral
∫
−
2
0
f
(
x
)
dx is equal to
A.
3
B.
5
C.
-3
D.
2
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q8.
If f (x) = f (a –x), then ,
∫
0
a
x
f
(
x
)
d
x
is equal to
A.
−
a
2
2
∫
0
a
f
(
x
)
d
x
B.
∫
0
a
f
(
x
)
d
x
C.
a
2
∫
0
a
f
(
x
)
d
x
D.
a
2
2
∫
0
a
f
(
x
)
d
x
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q9.
∫
cos
4
x
+
1
cot
x
+
tan
x
d
x
is equal to
A.
-
1
6
cos
3
2
x
+
C
B.
1
6
cos
3
2
x
+
C
C.
−
1
2
sin
2
6
x
+
C
D.
−
1
6
sin
3
2
x
+
C
View Solution
Add Work Space
Answer :
Option A
Explaination / Solution:
# Integrals
# CBSE 12th Mathematics
Prepare / Learn
Q10.
∫
0
π
1
−
cos
x
−
−
−
−
−
−
−
√
is equal to
A.
√3/2
B.
2
C.
2√2
D.
1
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
=
2
–
√
∫
0
π
sin
x
2
d
x
=
2
–
√
[
−
cos
x
2
1
2
]
π
0
=
−
2
2
–
√
[
cos
π
2
−
cos
0
]
=
2
2.
−
−
√
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