Mathematics

$$y=\displaystyle\int \cos\left\{2\tan^{-1}\sqrt{\dfrac{1-x}{1+x}}\right\}dx$$ is an equation of a family of?


ANSWER

Parabolas


SOLUTION
Putting $$x=\cos 2\theta$$
$$\therefore \cos\left\{2\tan^{-1}\sqrt{\dfrac{1-x}{1+x}}\right\}=\cos 2\theta =x$$
$$\therefore y=\displaystyle\int xdx=\dfrac{x^2}{2}+c$$.
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Single Correct Medium Published on 17th 09, 2020
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