If ∫ (1/x) √((1−x)/(1+x)) dx... | JEE Main 2022

JEE MAIN 2022

26-06-22 S2

Question

If $\int \frac{1}{x} \sqrt{\frac{1-x}{1+x}} d x=g(x)+c, g(1)=0$, then $g\left(\frac{1}{2}\right)$ is equal to :

Select the correct option:

$\log _e\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)+\frac{\pi}{3}$

$\log _e\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)+\frac{\pi}{3}$

$\log _e\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)-\frac{\pi}{3}$

$\frac{1}{2} \log _e\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)-\frac{\pi}{6}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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