Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
JEE Advanced 2015 Paper 1 Mathematics Q8
Mathematics
Problem
Let
F
(
x
)
=
∫
x
x
2
+
π
/
6
2
cos
2
t
d
t
F(x)=\displaystyle\int_x^{x^2+\pi/6}2\cos^2t\,dt
F
(
x
)
=
∫
x
x
2
+
π
/6
2
cos
2
t
d
t
for all
x
∈
R
x\in\mathbb R
x
∈
R
and
f
:
[
0
,
1
2
]
→
[
0
,
∞
)
f:\left[0,\frac12\right]\to[0,\infty)
f
:
[
0
,
2
1
]
→
[
0
,
∞
)
be a continuous function. For
a
∈
[
0
,
1
2
]
a\in\left[0,\frac12\right]
a
∈
[
0
,
2
1
]
, if
F
′
(
a
)
+
2
F'(a)+2
F
′
(
a
)
+
2
is the area of the region bounded by
x
=
0
x=0
x
=
0
,
y
=
0
y=0
y
=
0
,
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
and
x
=
a
x=a
x
=
a
, then
f
(
0
)
f(0)
f
(
0
)
is
Browse the problem library