CBSE 2026 · Region 2 · Set 1 · Q26 · 3 marks
Find : $\displaystyle \int \frac{x+2}{\sqrt{9 x-x^{2}}} \mathrm{~d} x$
Marking-scheme solution
$\displaystyle I=\int \dfrac{x+2}{\sqrt{9x-x^{2}}}\, dx$
Let $\displaystyle x+2=A(9-2x)+B$
$\displaystyle \Rightarrow A=-\dfrac{1}{2}, B=\dfrac{13}{2}$
$\displaystyle I=-\dfrac{1}{2}\int \dfrac{9-2x}{\sqrt{9x-x^{2}}}\, dx+\dfrac{13}{2}\int \dfrac{1}{\sqrt{9x-x^{2}}}\, dx$
$\displaystyle =-\dfrac{1}{2}\left(2\sqrt{9x-x^{2}}\right)+\dfrac{13}{2}\int \dfrac{1}{\sqrt{\left(\dfrac{9}{2}\right)^{2}-\left(x-\dfrac{9}{2}\right)^{2}}}\, dx$
$\displaystyle =-\sqrt{9x-x^{2}}+\dfrac{13}{2} \sin^{-1}\left(\dfrac{2x-9}{9}\right)+C$
IntegralsIntegrals of Some Particular FunctionsApplyshort_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.