$\mathop \smallint \nolimits_\alpha ^\beta \,\,\sqrt {\frac{{x\,\, - \,\,\alpha }}{{\beta \,\, - \,\,x}}} \,\,dx$ is equal to

$\frac{\pi }{2}\,\,\left( {\alpha - \beta } \right)$

$\pi \,\,\left( {\alpha - \beta } \right)$

$\pi {\mkern 1mu} {\mkern 1mu} \left( {\beta - \alpha } \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

\int \nolimits_\alpha ^\beta \,\,\sqrt {\frac{{x\,\, - \,\,\alpha }}{{\beta \,\, - \,\,x}}} \,\,dx

is equal to

View answer and explanation

Correct option: B

\frac{\pi }{2}\,\,\left( {\beta - \alpha } \right)

Option D (

\pi \left( {\beta - \alpha } \right)

) is incorrect. Option B (

\frac{\pi }{2}\,\left( {\beta - \alpha } \right)

) is correct because the integral evaluates to

\frac{\pi}{2}(\beta - \alpha)

after substitution and simplification.

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)