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MCQMediumJEE Main 2023 · 31 January, Shift 2Definite Integrals

Mathematics Question from JEE Main 2023 · 31 January, Shift 2

If ϕ(x)=1x∫π4x(42sin⁡t−3ϕ′(t)) dt, x>0,\phi(x) = \frac{1}{\sqrt{x}} \int_{\frac{\pi}{4}}^{x} \left( 4\sqrt{2} \sin t - 3 \phi'(t) \right) \, dt, \, x > 0,

then ϕ′(π4)\phi'\left( \frac{\pi}{4} \right) is equal to:

  • A

    8π\frac{8}{\sqrt{\pi}}

  • B

    46+π\frac{4}{6 + \sqrt{\pi}}

  • C

    86+π\frac{8}{6 + \sqrt{\pi}}

  • D

    46−π\frac{4}{6 - \sqrt{\pi}}

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