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Question
Evaluate:
`int_(π/4)^(π/2) cot^2x dx`.
Sum
Solution
`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`.
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Methods of Evaluation and Properties of Definite Integral
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