If $b\,\,\, > \,\,a$, then $\mathop \smallint \nolimits_a^b \,\,\frac{{dx}}{{\sqrt {\left( {x - a} \right)\,\,\left( {b - x} \right)} }}$ is equal to

$\frac{\pi }{2}\left( {b - a} \right)$

$\frac{\pi }{4}\left( {b - a} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

b\,\,\, > \,\,a

, then

\int \nolimits_a^b \,\,\frac{{dx}}{{\sqrt {\left( {x - a} \right)\,\,\left( {b - x} \right)} }}

is equal to

View answer and explanation

Correct option: B

\pi

Option B (

\pi

) is correct because it is the value obtained after evaluating the definite integral using trigonometric substitution.

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