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If $Δ (x) = |\begin{matrix} 1 & \cos x & 1 - \cos x \\ 1 + \sin x & \cos x & 1 + \sin x - \cos x \\ \sin x & \sin x & 1 \end{matrix}|$ then $\int_{0}^{π / 2} Δ (x) d x$ equal

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Correct option is D

Using , C1→C1-C2-C3, we get Δ(x)=0cosx1-cosx0cosx1+sinx-cosx-1sinx1=(-1)cosx1-cosxcosx1+sinx-cosx=(-1)cosx[1+sinx-cosx-1+cosx]=-cosxsinx=-12(sin2x)∴ ∫0π/2Δ(x)dx=-12(-1)2cos2x0π/2=14(cosπ-cos0)=-12

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If Δ(x)=1cosx1-cosx1+sinxcosx1+sinx-cosxsinxsinx1 then ∫0π/2Δ(x)dx equal

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If $Δ (x) = |\begin{matrix} 1 & \cos x & 1 - \cos x \\ 1 + \sin x & \cos x & 1 + \sin x - \cos x \\ \sin x & \sin x & 1 \end{matrix}|$ then $\int_{0}^{π / 2} Δ (x) d x$ equal