If ∫ (π)/6 ^((π)/3) √(1- sin 2 x) d x=α+β √(2)+γ √(3), where α, β and γ are rational numbers, then 3 α+4 β-γ is equal to _ _ _ _ _.

Integral Calculus: JEE Main 2024 Mathematics question

JEE Main 2024 · 29 Jan, Evening shift · Q34

JEE Main 202429 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}

, where

\alpha, \beta

and

\gamma

are rational numbers, then

3 \alpha+4 \beta-\gamma

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2024 Integral Calculus Question with Answer (29 Jan Evening shift, Q34) | JEE Arc