Evaluate: `int_0^(10pi)[tan^(-1)x]dx ,w h e r e[x]` represents greatest integer function.

Evaluate: `int_0^(10pi)[tan^(-1)x]dx ,w h e r e[x]` represents greatest integer function.

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

We have `{(0,lt tan^(-1)xlt1,,,"when"0ltxlttan1),(1,lt tan^(-1)xlt(pi)/2,,,"when" tan1ltxlt10pi):}`
`:.I=int_(0)^(10pi)[tan^(-1)x]dx=int_(0)^(tan1) 0 dx+int_(tan1)^(10pi) 1dx=10 pi-tan1`

4 views Answered 2023-02-05 15:29

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