Let f be a non-negative function defined on the interval [0, 1]. If \int^{x}_{0}\sqrt{1-(f'(t))^2} dt = \int^{x}_{0} f (t) dt , 0 ≤ x ≤ 1, and f (0) = 0 , then [JEE Adv 2009 P1]

Correct Answer is : f (12) < 12 and f (13) < 13

f (1/2) < 1/2 and f (1/3) > 1/3

f (1/2) > 1/2 and f (1/3) > 1/3

f (1/2) < 1/2 and f (1/3) < 1/3

f (1/2) > 1/2 and f (1/3) < 1/3

Application of Integration

Section: Mathematics

Question : 26 of 28

Marks: +1, -0

Let f be a non-negative function defined on the interval [0, 1]. If

∫

√1−(f′(t))2dt =

∫

f (t) dt , 0 ≤ x ≤ 1, and f (0) = 0 , then

[JEE Adv 2009 P1]

Go to Question:

Prev Question

Next Question