The value of the integral $\mathop \smallint \limits_\alpha ^\beta \,\,\frac{1}{{\sqrt {\left( {x - \alpha } \right)\,\,\left( {\beta - x} \right)} }}\,\,dx$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_\alpha ^\beta \,\,\frac{1}{{\sqrt {\left( {x - \alpha } \right)\,\,\left( {\beta - x} \right)} }}\,\,dx

, is

View answer and explanation

Correct option: C

\pi

Option C

\pi

is correct because the integral evaluates to

\pi

after a suitable trigonometric substitution.

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