Let $\smallint \,\,\sqrt {\frac{{5\,\, - \,\,x}}{{2\,\, + \,\,x}}} \,\,dx$ equal

$\sqrt {x + 2} \,\,\sqrt {5 - x} \,\, + \,\,3\,\,{\sin ^{ - 1}}\,\,\sqrt {\frac{{x + 2}}{3}} + C$

$\sqrt {x + 2} \,\,\sqrt {5 - x} \,\, + \,\,5\,\,{\sin ^{ - 1}}\,\,\sqrt {\frac{{x + 2}}{5}} + C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

Let

\int \,\,\sqrt {\frac{{5\,\, - \,\,x}}{{2\,\, + \,\,x}}} \,\,dx

equal

View answer and explanation

Correct option: B

\sqrt {x + 2} \,\,\sqrt {5 - x} \,\, + \,\,7\,\,{\sin ^{ - 1}}\,\,\sqrt {\frac{{x + 2}}{7}} + C

Option B (

\sqrt {x + 2} \,\sqrt {5 - x} \, + \,7\,{\sin ^{ - 1}}\,\sqrt {\frac{{x + 2}}{7}} \, + C

) is correct because after substituting

2 + x = t^2

, the integral can be solved using standard integral formulas.