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Calculus Level 2

If for a real number y, [y] is the greatest integer less than or equal to y, then the value of the integral ∫ π / 2 3 π / 2 [ 2 sin ⁡ x ] ∂ x \int _{ \pi /2 }^{ 3\pi /2 }{ \left[ 2\quad \sin { x } \right] } \partial x is :

π 2 \frac { \pi }{ 2 } − π 2 \frac { -\pi }{ 2 } − π 4 \frac { -\pi }{ 4 } 0

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Varun Suvarna by Varun Suvarna , 23, India

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