PARAGRAPH – 2
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 \( g(x) = \sqrt{\frac{\pi x}{2} - x^{2}} \).
The value of \( 2 \int_{0}^{\pi/2} f(x) g(x) \, dx - \int_{0}^{\pi/2} g(x) \, dx \) is ____________.
