If $f\,\,\left( x \right)$ is a function satisfying $f\left( {\frac{1}{x}} \right)\,\, + \,\,{x^2}\,f\left( x \right) = 0$ for all non-zero $x$, then $\mathop \smallint \nolimits_{\sin \,\,{\rm{\theta }}}^{{\rm{cosec \theta }}} \,\,f\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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f\,\,\left( x \right)

is a function satisfying

f\left( {\frac{1}{x}} \right)\,\, + \,\,{x^2}\,f\left( x \right) = 0

for all non-zero

x

, then

\int \nolimits_{\sin \,\,\mathrm{\theta }}^{\mathrm{cosec \theta }} \,\,f\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: A

\mathrm{0}

Option A (0) is correct because using the substitution x = 1/t and the given functional equation, the integral becomes its negative, implying it equals zero.

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[*]

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