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Application of Integration question

2015 · Shift 2 · Q26

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PYQ Library
JEE Advanced
Mathematics
Application of Integration
2015 · Shift 2 · Q26

Application of Integration question

2015 · Shift 2 · Q26

JEE AdvancedMathematicsApplication of IntegrationNumerical+4 / −1

Let

f:R \to R

be a continuous odd function, which vanishes exactly at one point and

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

Suppose that

F\left( x \right) = \int\limits_{ - 1}^x {f\left( t \right)dt}

for all

x \in \,\,\left[ { - 1,2} \right]

and

G(x)=

\int\limits_{ - 1}^x {t\left| {f\left( {f\left( t \right)} \right)} \right|} dt

for all

x \in \,\,\left[ { - 1,2} \right].

If

\mathop {\lim }\limits_{x \to 1} {{F\left( x \right)} \over {G\left( x \right)}} = {1 \over {14}},

then the value of

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

is

Numerical answer

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