Mathematics

Integrate : $$\sqrt{\dfrac{2 - x}{x}} \, (0 < x < 2)$$


SOLUTION
$$\int \sqrt{\dfrac{2-x}{x}}dx$$

$$u=\sqrt{\dfrac{2-x}{x}},v'=1$$

$$=\sqrt{\dfrac{2-x}{x}}x-\int -\dfrac{1}{x^{\frac{1}{2}}\sqrt{2-x}}dx$$

$$=x\sqrt{\dfrac{2-x}{x}}+2\sin^{-1}\left ( \dfrac{1}{\sqrt{2}}\sqrt{x} \right )$$

$$=x\sqrt{\dfrac{2-x}{x}}+2\sin^{-1}\left ( \sqrt{\dfrac{x}{2}} \right )+C$$
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Subjective Medium Published on 17th 09, 2020
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