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MathsJEE Main 4 Apr 2026, Shift 1·Q19·MCQ·Tough

Definite Integration · Integral with greatest integer function

Let ∫−22(∣sin⁡x∣+[xsin⁡x])dx=2(3−cos⁡2)+β\displaystyle\int_{-2}^{2}\left(\lvert\sin x\rvert + [x\sin x]\right)dx = 2(3 - \cos 2) + \beta, where [⋅][\cdot] is the greatest integer function. Then βsin⁡(β2)\beta\sin\left(\dfrac{\beta}{2}\right) equals.
  1. (1)1
  2. (2)2
  3. (3)4
  4. (4)8

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