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प्रश्न
Evaluate: `int_0^(π/4) cot^2x.dx`
उत्तर
`int_0^(π/4) cot^2x.dx`
= `int_0^(π/4) ("cosec"^2x - 1).dx`
= `int_0^(π/4) "cosec"^2x.dx - int_0^(π/4)1.dx`
= `[-cot x]_0^(π/4) - [x]_0^(π/4)`
= `[(-cot π/4) - (-cot 0)] - [π/4 - 0]`
= `-1 + cot 0 - pi/4`
The integral does not exist since cot 0 is not defined.
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