Let \(\int_{-2}^2(|\sin x|+[x \sin x]) d x=2(3-\cos 2)+\beta\) where \([\cdot ]\) is the greatest integer function. Then…

Let \(\int_{-2}^2(|\sin x|+[x \sin x]) d x=2(3-\cos 2)+\beta\) where \([\cdot ]\) is the greatest integer function. Then \(\beta \sin \left(\frac{\beta }{2}\right)\)equals:

[JEE Main 2026, 4 Apr (Shift 1)]