If 525∫₀^(π/2) sin 2x cos^(11/2) x (1 + cos^(5/2) x)^(1/2) dx = (… | JEE Main 2024 Mathematics PYQ | Jeeify

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MCQMediumJEE Main 2024 · 31 January, Shift 1Definite Integrals

If

525\int_{0}^{\frac{\pi}{2}} \sin 2x\, \cos^{\frac{11}{2}} x \left(1 + \cos^{\frac{5}{2}} x\right)^{\frac{1}{2}} dx = \left(n\sqrt{2} - 64\right),

then $n$ is equal to:

A
$176$
B
$150$
C
$100$
D
$80$

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