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Calculus Level 3

\(Consider\\ L=\sqrt [ 3 ]{ 2012 } +\sqrt [ 3 ]{ 2013 } +....+\sqrt [ 3 ]{ 3011 } \\ R=\sqrt [ 3 ]{ 2013 } +\sqrt [ 3 ]{ 2014 } +....+\sqrt [ 3 ]{ 3012 } \\ and\quad I=\int _{ 2012 }^{ 3012 }{ \sqrt[3]{ x } dx } \)

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