NVAMediumJEE Main 2025 · 29 January, Shift 2Indefinite Integrals

Mathematics Question from JEE Main 2025 · 29 January, Shift 2

If 240π4(sin4xπ12+[2sinx])dx=2π+α,24 \int_0^{\frac{\pi}{4}} \left( \sin\left|4x - \frac{\pi}{12}\right| + [2 \sin x] \right) dx = 2\pi + \alpha, where [][\,\cdot\,] denotes the greatest integer function, then α\alpha is equal to:

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