Let $f\;:R \to R,\,\;g\;:R \to R$ be continuous functions. Then the value of the integral $\mathop \smallint \limits_{ - \pi /2}^{\pi /2} \,\,\left[ {\,f\left( x \right)\,\, + \,\,f\left( { - x} \right)} \right]\,\,\left[ {\,\,g\,\,\left( x \right) - \,\,g\left( {\, - \,x} \right)} \right]\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Understanding +4 | -1

Let

f\;:R \to R,\,\;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

View answer and explanation

Correct option: D

\mathrm{0}

Option D (0) is correct because the integrand is an odd function integrated over a symmetric interval.

Practice All Chapter MCQs →

\int \nolimits_0^\infty \,\,\log \,\,\left( {x + \frac{1}{x}} \right)\,\,\frac{{dx}}{{1 + {x^2}}}

f\left( x \right)

\int \nolimits_0^{{t^2}} \,\,x\;\,f\left( x \right)\,\,dx = \frac{2}{5}\,\,{t^5}

f\left( {\frac{4}{{25}}} \right)

\int\limits_{{0}}^{11}[x]^{3} . \mathrm{dx}

[*]

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)