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Question: Evaluate : \(\int _ { 0 } ^ { 102 } \left[ \tan ^ { - 1 } x \right]\)dx, where [·] denotes the great...

Evaluate : ∫0102[tan⁡−1x]\int _ { 0 } ^ { 102 } \left[ \tan ^ { - 1 } x \right]dx, where [·] denotes the greatest integer function less than or equal to x -

A

102 – tan 2

B

102 – tan 1

C

101 – tan 2

D

None of these

Answer

102 – tan 1

Explanation

Solution

∫0102[tan⁡−1x]\int _ { 0 } ^ { 102 } \left[ \tan ^ { - 1 } x \right]dx

= dx +

= 0 + 1.

= 102 – tan 1.