Differentiable Function and Integral Relation (… | ExamDuo
Ask Doubts
Log in
Basics and Substitution
Hard
Differentiable Function and Integral Relation
Let
g
:
(
0
,
∞
)
→
R
be a differentiable function such that
∫
(
x
(
cos
x
−
sin
x
)
e
x
+
1
+
g
(
x
)
(
e
x
+
1
−
x
e
x
)
(
e
x
+
1
)
2
)
d
x
=
x
g
(
x
)
e
x
+
1
+
c
, for all
x
>
0
, where
c
is an arbitrary constant. Then :
Ask about this question
SELECT ONE OPTION
A
g
is decreasing in
(
0
,
π
4
)
B
g
′
is increasing in
(
0
,
π
4
)
C
g
+
g
′
is increasing in
(
0
,
π
2
)
D
g
−
g
' is increasing in
(
0
,
π
2
)
Check