Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
JEE Advanced 2014 Paper 2 Mathematics Q4
Mathematics
Problem
Let
f
:
[
0
,
2
]
→
R
f:[0,2]\to\mathbb R
f
:
[
0
,
2
]
→
R
be a function which is continuous on
[
0
,
2
]
[0,2]
[
0
,
2
]
and is differentiable on
(
0
,
2
)
(0,2)
(
0
,
2
)
with
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
. Let
F
(
x
)
=
∫
0
x
2
f
(
t
)
d
t
\displaystyle F(x)=\int_0^{x^2}f(\sqrt t)\,dt
F
(
x
)
=
∫
0
x
2
f
(
t
)
d
t
for
x
∈
[
0
,
2
]
x\in[0,2]
x
∈
[
0
,
2
]
. If
F
′
(
x
)
=
f
′
(
x
)
F'(x)=f'(x)
F
′
(
x
)
=
f
′
(
x
)
for all
x
∈
(
0
,
2
)
x\in(0,2)
x
∈
(
0
,
2
)
, then
F
(
2
)
F(2)
F
(
2
)
equals
Browse the problem library