JEE MAIN - Mathematics Hindi (2022 - 26th June Evening Shift - No. 7)
यदि $$\int \frac{1}{x} \sqrt{\frac{1-x}{1+x}} d x=g(x)+c, g(1)=0$$ हैं, तो $$g\left(\frac{1}{2}\right)$$ बराबर है-
$$\log _{e}\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)+\frac{\pi}{3}$$
$$\log _{e}\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)+\frac{\pi}{3}$$
$$\log _{e}\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)-\frac{\pi}{3}$$
$$
\frac{1}{2} \log _{e}\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)-\frac{\pi}{6}
$$
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