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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Find the integral: $\int \frac{d x}{\sqrt{2 x-x^{2}}}$
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Answer

Let I = $\int \frac{d x}{\sqrt{2 x-x^{2}}}$
$= \int \frac{d x}{\sqrt{1-(x-1)^{2}}}$
Put $x - 1 = t.$ Then $dx = dt.$
Therefore, $\int \frac{d x}{\sqrt{2 x-x^{2}}}=\int \frac{d t}{\sqrt{1-t^{2}}}=\sin ^{-1}(t)+C$
$= \sin^{-1} (x-1) + C$

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