When using trigonometric substitution in calculus you're supposed to always keep in mind the domain of the angle. In the case of √(x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}-a^{2}) (where "a" is a number >0) you use x=a⋅arcsec Θ for the substitution.

For trigonometric substitution, textbooks state that the domain of Θ must be {0≤Θ<π/2} ∪ {π/2<Θ≤π} when using the x=a⋅arcsec Θ substitution. Some textbooks alternatively give the allowable domain as {0≤Θ<π/2} ∪ {π≤Θ<3π/2} instead. In either case, there are issues which don't seem to make sense to me.

Please see the attached PDF file for my questions.

Thank you.

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# Understanding Trigonometric Substitution

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