JEE Advance - Mathematics (1990 - No. 26)
Let $$f:R \to R$$ and $$\,\,g:R \to R$$ be continuous functions. Then the value of the integral
$$\int\limits_{ - \pi /2}^{\pi /2} {\left[ {f\left( x \right) + f\left( { - x} \right)} \right]\left[ {g\left( x \right) - g\left( { - x} \right)} \right]dx} $$ is
$$\int\limits_{ - \pi /2}^{\pi /2} {\left[ {f\left( x \right) + f\left( { - x} \right)} \right]\left[ {g\left( x \right) - g\left( { - x} \right)} \right]dx} $$ is
$$\pi $$
$$1$$
$$-1$$
$$0$$