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Indefinite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\sqrt{3-\text{x}^2}\text{dx}$
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Answer

Let $\text{I}=\int\sqrt{3-\text{x}^2}\text{dx}$
$=\int\sqrt{(\sqrt3)^2-\text{x}^2}\text{dx}$
$\text{I}=\frac{\text{x}}{2}\sqrt{3-\text{x}^2}+\frac{3}{2}\sin^{-1}\Big(\frac{\text{x}}{\sqrt3}\Big)+\text{C}$

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