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Definite Integration

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Let

f: \left[0, \frac{\pi}{2}\right] \to [0,1]

be the function defined by

f(x)=\sin^2 x

and let

g: \left[0, \frac{\pi}{2}\right] \to [0, \infty]

be the function defined by

g(x)=\sqrt{\frac{\pi x}{2} - x^2}

.

Section: Mathematics

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Question : 3 of 46

Marks: +1, -0

The value of

\; \frac{16}{\pi^3} \int\limits_{0}^{\;\frac{\pi}{2}} f(x) g(x) dx

[JEE Adv 2024 P2]

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