QJEEM24Ma9758: JEE Main 2024 Mathematics - Class 12 JEEM24Ma9758 Solution: If ∫ π 6 π 3 1 − sin ⁡ 2 x d x = α + β 2 + γ 3 , where α , β…

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QJEEM24Ma9758: JEE Main 2024 Mathematics - Class 12 JEEM24Ma9758 Solution: If ∫ π 6 π 3 1 − sin ⁡ 2 x d x = α + β 2 + γ 3 , where α , β…

If $\int_{\frac{π}{6}}^{\frac{π}{3}} \sqrt{1 - \sin 2 x} d x = α + β \sqrt{2} + γ \sqrt{3}$ , where $α, β$ and $γ$ are rational numbers, then $3 α + 4 β - γ$ is equal to _________.

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$\begin{aligned} = \int_{\frac{π}{6}}^{\frac{π}{3}} \sqrt{1 - \sin 2 x} d x \\ = \int_{\frac{π}{6}}^{\frac{π}{3}} | \sin x - \cos x | d x \\ = \int_{\frac{π}{6}}^{\frac{π}{4}} (\cos x - \sin x) d x + \int_{\frac{π}{4}}^{\frac{π}{3}} (\sin x - \cos x) d x \\ = - 1 + 2 \sqrt{2} - \sqrt{3} \\ = α + β \sqrt{2} + γ \sqrt{3} \\ α = - 1, β = 2, γ = - 1 \\ 3 α + 4 β - γ = 6 \end{aligned}$

QJEEM24Ma9758: JEE Main 2024 Mathematics - Class 12 JEEM24Ma9758 Solution: If ∫ π 6 π 3 1 − sin ⁡ 2 x d x = α + β 2 + γ 3 , where α , β…

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