If $f:R \to R$ and ${\rm{g}}:R \to R$ are one to one, real valued functions, then the value of the integral $\mathop \smallint \nolimits_{ - \pi }^\pi \,\,\,\left[ {f\left( x \right)\,\, + \,\,f\,\left( { - x} \right)} \right]\,\,\left[ {{\rm{g}}\,\,\left( x \right)\,\, - \,\,{\rm{g}}\,\,\left( { - x} \right)} \right]\,\,dx$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f:R \to R

and

\mathrm{g}:R \to R

are one to one, real valued functions, then the value of the integral

\int \nolimits_{ - \pi }^\pi \,\,\,\left[ {f\left( x \right)\,\, + \,\,f\,\left( { - x} \right)} \right]\,\,\left[ {\mathrm{g}\,\,\left( x \right)\,\, - \,\,\mathrm{g}\,\,\left( { - x} \right)} \right]\,\,dx

View answer and explanation

Correct option: A

\mathrm{0}

Option A (0) is correct because the integrand is an odd function, and the integral of an odd function over a symmetric interval is zero.