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The value of the integral \({\int }_{-1}^{1}{\log }_{e}(\sqrt{1-x}+\sqrt{1+x})dx\) is equal to: [JEE Main 2021, 20 Jul (…

Q1

The value of the integral \({\int }_{-1}^{1}{\log }_{e}(\sqrt{1-x}+\sqrt{1+x})dx\) is equal to:

[JEE Main 2021, 20 Jul (Shift 1)]

a

\(2 \log _e 2+\frac{\pi}{4}-1\)

b

\(\log _e 2+\frac{\pi}{2}-1\)

c

\(\frac{1}{2} \log _e 2+\frac{\pi}{4}-\frac{3}{2}\)

d

\(2 \log _e 2+\frac{\pi}{2}-\frac{1}{2}\)

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