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JEE Advance 2013
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Question
Let $f:\left[\frac{1}{2}, 1\right] \rightarrow R$ (the set of all real numbers) be a positive, non-constant and differentiable function such that $f^{\prime}(x)<2 f(x)$ and $f\left(\frac{1}{2}\right)=1$. Then the value of $\int_{1 / 2}^1 f(x) d x$ lies in the interval
Select the correct option:
A
$(2 \mathrm{e}-1,2 \mathrm{e})$
B
$(e-1,2 e-1)$
C
$\left(\frac{e-1}{2}, e-1\right)$
D
$\left(0, \frac{e-1}{2}\right)$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
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JEE Advance
Mathematics
Easy
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