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If f(x) is a function satisfying f(1/x)+...

If `f(x)` is a function satisfying `f(1/x)+x^2f(x)=0` for all nonzero `x` , then evaluate `int_(sintheta)^(cos e ctheta)f(x)dx`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` l = int _(sin theta)^("cosec" theta) f(x) dx , `
Put `x = 1/t rArr dx = -1/(t^(2)) dt`
` :. l = - int _("cosec" theta)^(sin theta) f(1/t) .1/(t^(2)) dt = int _(sin theta)^("cosec" theta) 1/(x^(2))f(1/x)dx`
` rArr l = -int _(sin theta)^("cosec" theta) f(x) dx`
` rArr l = 0 [ :' f(1/x) = -x^(2) f(x)]`
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