Limit Integral Non-negative Function (Jee Mains) | ExamDuo
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First Order Differential Equations
Medium
Limit Integral Non-negative Function
Let f be a non-negative function in
[
0
,
1
]
and twice differentiable in
(
0
,
1
)
. If
∫
0
x
√
1
−
(
f
′
(
t
)
)
2
d
t
=
∫
0
x
f
(
t
)
d
t
,
0
≤
x
≤
1
and
f
(
0
)
=
0
, then
lim
x
→
0
1
x
2
∫
0
x
f
(
t
)
d
t
Ask about this question
SELECT ONE OPTION
A
equals 0
B
equals 1
C
does not exist
D
equals
1
2
Check