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A function `y = f(x)` satisfies the condition `f'(x) sin x + f(x) cos x=1 ,f(x)` being bounded when `x->0`. If `I= int_0^(pi/2) f(x) dx` then (A) `pi/2ltIltpi^2/4` (B) `pi/4ltIltpi^2/2` (C) `1ltIltpi/2` (D)`0ltIlt1`

A

`(pi)/(2)ltIlt(pi^(2))/(4)`

B

`(pi)/(4)ltIlt(pi^(2))/(2)`

C

`1ltIlt(pi)/(2)`

D

`0ltIlt1`

Text Solution

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A
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