Question

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Answer 1

$\int\limits^\frac{\pi }{2} _\frac{\pi }{4}{Sin2x} \, dx=-\frac{1}{2}Cos2x|^{\frac{\pi}{2}}_{\frac{\pi }{4}}=-\frac{1}{2}[Cos(2*\frac{\pi }{2})-Cos(2*\frac{\pi }{4})]=\\=-\frac{1}{2}(Cos\pi-Cos\frac{\pi }{2})=-\frac{1}{2}(-1-0)=\frac{1}{2}$