Question

Evaluate:

`int_(π/4)^(π/2) cot^2x  dx`.

Answer 1

`int_(π/4)^(π/2) cot^2x  dx`

= `int_(π/4)^(π/2) ("cosec"^2x - 1)dx`

= `int_(π/4)^(π/2) "cosec"^2x dx - int_(π/4)^(π/2) 1 dx`

= `[-cot x]_(π/4)^(π/2) - [x]_(π/4)^(π/2)`

= `[(-cot  π/2) - (- cot  π/4)] - [π/2 - π/4]`

= `[-0 - (-1)] - π/4`

= `1 - π/4`.