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Definite Integration question

2014 · Shift 2 · Q39

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2014 · Shift 2 · Q39

Definite Integration question

2014 · Shift 2 · Q39

JEE AdvancedMathematicsDefinite IntegrationMCQ+3 / −1

Given that for each

a \in \left( {0,1} \right),\,\,\,\mathop {\lim }\limits_{h \to {0^ + }} \,\int\limits_h^{1 - h} {{t^{ - a}}{{\left( {1 - t} \right)}^{a - 1}}dt}

exists. Let this limit be

g(a).

In addition, it is given that the function

g(a)

is differentiable on

(0,1).

The value of

g\left( {{1 \over 2}} \right)

is

A
$\pi$
B
$2\pi$
C
${\pi \over 2}$
D
${\pi \over 4}$

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