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Let f be a non - negative function on th...

Let f be a non - negative function on the interval [0,1] . If `int_(0)^(x)sqrt(1-(f'(t)))^(2)dt=int_(0)^(x)f(t)dt,0lexle1andf(0)=0` then

A

`f((1)/(2))lt(1)/(2)andf((1)/(3))gt(1)/(3)`

B

`f((1)/(2))gt(1)/(2)andf((1)/(3))gt(1)/(3)`

C

`f((1)/(2))lt(1)/(2)andf((1)/(3))lt(1)/(3)`

D

`f((1)/(2))gt(1)/(2)andf((1)/(3))lt(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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