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MCQMediumJEE Main 2023 · 11 April, Shift 2Properties of Definite Integrals

Mathematics Question from JEE Main 2023 · 11 April, Shift 2

If f:R→Rf : \mathbb{R} \to \mathbb{R} is a continuous function satisfying

∫0π2f(sin⁡2x)sin⁡x dx+α∫0π4f(cos⁡2x)cos⁡x dx=0,\int_{0}^{\frac{\pi}{2}} f(\sin 2x) \sin x \, dx + \alpha \int_{0}^{\frac{\pi}{4}} f(\cos 2x) \cos x \, dx = 0,

then the value of α\alpha is:

  • A

    −3-\sqrt{3}

  • B

    3\sqrt{3}

  • C

    −2-\sqrt{2}

  • D

    2\sqrt{2}

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