Definite IntegrationHard
Question
If f(x) is a function satisfying f (1/x) + x2 f(x) = 0 for all non-zero x, then 
dx equals to :
dx equals to :Options
A.sinθ + cosecθ
B.sin2 θ
C.cosec2 θ
D.none of these
Solution
f(1/x) + x2 f(x) = 0 ⇒ f(x) = - 
dx
⇒ I =
put 1/x = t ⇒ -1/x2 dx = dt
⇒ I =
⇒ I = - 
= - 1
⇒ 2 I = 0 ⇒ I = 0
dx⇒ I =
put 1/x = t ⇒ -1/x2 dx = dt
⇒ I =
⇒ I = - = - 1⇒ 2 I = 0 ⇒ I = 0
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