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Application of Integration question

2009 · Shift 1 · Q29

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PYQ Library
JEE Advanced
Mathematics
Application of Integration
2009 · Shift 1 · Q29

Application of Integration question

2009 · Shift 1 · Q29

JEE AdvancedMathematicsApplication of IntegrationMCQ+3 / −1

Let

f

be a non-negative function defined on the interval

[0,1]

. If

\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}dt} = \int\limits_0^x {f(t)dt,0 \le x \le 1} }

, and

f(0) = 0

, then

A
$f\left( {{1 \over 2}} \right) \lt {1 \over 2}$ and $f\left( {{1 \over 3}} \right) \gt {1 \over 3}$
B
$f\left( {{1 \over 2}} \right) \gt {1 \over 2}$ and $f\left( {{1 \over 3}} \right) \gt {1 \over 3}$
C
$f\left( {{1 \over 2}} \right) \lt {1 \over 2}$ and $f\left( {{1 \over 3}} \right) \lt {1 \over 3}$
D
$f\left( {{1 \over 2}} \right) \gt {1 \over 2}$ and $f\left( {{1 \over 3}} \right) \lt {1 \over 3}$

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