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Definite Integration question

2013 · Shift 1 · Q35

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2013 · Shift 1 · Q35

Definite Integration question

2013 · Shift 1 · Q35

JEE AdvancedMathematicsDefinite IntegrationMCQ+4 / −1

Let

f

:\,\,\left[ {{1 \over 2},1} \right] \to R

(the set of all real number) be a positive, non-constant and differentiable function such that

f'\left( x \right) \lt 2f\left( x \right)

and

f\left( {{1 \over 2}} \right) = 1.

Then the value of

\int\limits_{1/2}^1 {f\left( x \right)} \,dx

lies in the interval

A
$\left( {2e - 1,2e} \right)$
B
$\left( {e - 1,\,2e - 1} \right)$
C
$\left( {{{e - 1} \over 2},e - 1} \right)$
D
$\left( {0,{{e - 1} \over 2}} \right)$

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