If $\mathop \smallint \nolimits_0^\pi \,\,x\,\,{\rm{ }}f\,\,\left( {\sin \,\,x} \right)\,\,dx = A\,\,\mathop \smallint \nolimits_0^{\pi /2} \,\,f\,\,(\sin \,\,x)\,\,dx,{\rm{then}}\,\,A$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \nolimits_0^\pi \,\,x\,\,\mathrm{ }f\,\,\left( {\sin \,\,x} \right)\,\,dx = A\,\,\int \nolimits_0^{\pi /2} \,\,f\,\,(\sin \,\,x)\,\,dx,\mathrm{then}\,\,A

is equal to

View answer and explanation

Correct option: B

\pi

Option B (

\pi

) is correct because by using the property of definite integrals, the given integral can be expressed in terms of the integral from 0 to

\pi/2

, and A is found to be

\pi

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)