The value of the definite integral

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

The value of the definite integral ∫0π/2sin⁡∣2x−α∣ dx\int_0^{\pi/2}\sin|2x-\alpha|\,dx, where α∈[0,π]\alpha\in[0,\pi], is (1) 1 (2) cos⁡α\cos\alpha (3) 1+cos⁡α2\frac{1+\cos\alpha}{2} (4) 1−cos⁡α2\frac{1-\cos\alpha}{2}

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