If $f\left( x \right){\rm{\;}}\,\,{\rm{and}}\,\,\;g\left( x \right),\,\,\;x\, \in \,R$ are continuous functions, then value of integral $\mathop \smallint \nolimits_{ - \pi /2}^{\pi /2} \,\,\left[ {\left\{ {\,f\left( x \right)\,\, + \,\,f\left( { - x} \right)} \right\}\,\,\left\{ {g\left( x \right)\,\, - \,\,g\left( { - x} \right)} \right\}} \right]\;dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f\left( x \right)\mathrm{\;}\,\,\mathrm{and}\,\,\;g\left( x \right),\,\,\;x\, \in \,R

are continuous functions, then value of integral

\int \nolimits_{ - \pi /2}^{\pi /2} \,\,\left[ {\left\{ {\,f\left( x \right)\,\, + \,\,f\left( { - x} \right)} \right\}\,\,\left\{ {g\left( x \right)\,\, - \,\,g\left( { - x} \right)} \right\}} \right]\;dx

View answer and explanation

Correct option: D

\mathrm{0}

Option D (

\mathrm{0}

) is correct because the integrand is an odd function integrated over a symmetric interval.