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The value of \({\int }_{-\pi }^{\pi }\frac{2y(1+\sin y)}{1+{\cos }^{2}y}dy\) is: [JEE Main 2024, 5 Apr (Shift 1)]

Q1

The value of \({\int }_{-\pi }^{\pi }\frac{2y(1+\sin y)}{1+{\cos }^{2}y}dy\) is:

[JEE Main 2024, 5 Apr (Shift 1)]

a

\({\pi }^{2}\)

b

\(\frac{\pi }{2}\)

c

\(2{\pi }^{2}\)

d

\(\frac{{\pi }^{2}}{2}\)

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