Prove that $\int_{- \frac{π}{2}}^{2 π} [cot^{- 1} x] d x$ ,where\displaystyle{\left[{\dot}\right]} denotes the greatest integer function.

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Prove that

\int_{- \frac{π}{2}}^{2 π} [cot^{- 1} x] d x

,where\displaystyle{\left[{\dot}\right]} denotes the greatest integer function.

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Question Text

Prove that

\int_{- \frac{π}{2}}^{2 π} [cot^{- 1} x] d x

,where\displaystyle{\left[{\dot}\right]} denotes the greatest integer function.

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