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JEE Advanced 2013 Paper 1 Mathematics Q3
Mathematics
Problem
Let
f
:
[
1
/
2
,
1
]
→
R
f:[1/2,1]\to\mathbb{R}
f
:
[
1/2
,
1
]
→
R
(the set of all real numbers) be a positive, non-constant and differentiable function such that
f
′
(
x
)
<
2
f
(
x
)
f'(x)<2f(x)
f
′
(
x
)
<
2
f
(
x
)
and
f
(
1
/
2
)
=
1
f(1/2)=1
f
(
1/2
)
=
1
. Then the value of
∫
1
/
2
1
f
(
x
)
d
x
\displaystyle\int_{1/2}^{1} f(x)\,dx
∫
1/2
1
f
(
x
)
d
x
lies in the interval
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